diff --git a/.ghci b/.ghci deleted file mode 100644 --- a/.ghci +++ /dev/null @@ -1,1 +0,0 @@ -:set -isrc -idist/build/autogen -optP-include -optPdist/build/autogen/cabal_macros.h diff --git a/.gitignore b/.gitignore --- a/.gitignore +++ b/.gitignore @@ -1,4 +1,5 @@ dist +dist-newstyle docs wiki TAGS @@ -11,3 +12,21 @@ *.hi *~ *# +.stack-work/ +cabal-dev +*.chi +*.chs.h +*.dyn_o +*.dyn_hi +.hpc +.hsenv +.cabal-sandbox/ +cabal.sandbox.config +*.prof +*.aux +*.hp +*.eventlog +cabal.project.local +cabal.project.local~ +.HTF/ +.ghc.environment.* diff --git a/.hlint.yaml b/.hlint.yaml new file mode 100644 --- /dev/null +++ b/.hlint.yaml @@ -0,0 +1,7 @@ +- arguments: [-XCPP] + +- ignore: {name: Use fmap} +- ignore: {name: Avoid lambda} +- ignore: {name: Redundant lambda} +- ignore: {name: Unused LANGUAGE pragma} +- ignore: {name: Eta reduce, within: [Linear.Plucker, Linear.Quaternion, Linear.V, Linear.V0, Linear.V1, Linear.V2, Linear.V3, Linear.V4]} diff --git a/.travis.yml b/.travis.yml deleted file mode 100644 --- a/.travis.yml +++ /dev/null @@ -1,28 +0,0 @@ -language: haskell -before_install: - # Uncomment whenever hackage is down. - # - mkdir -p ~/.cabal && cp travis/config ~/.cabal/config && cabal update - - # Try installing some of the build-deps with apt-get for speed. - - travis/cabal-apt-install --only-dependencies --force-reinstall $mode - - - sudo apt-get -q -y install hlint || cabal install hlint - -install: - - cabal configure $mode - - cabal build - -script: - - $script - - hlint src --cpp-define HLINT - -notifications: - irc: - channels: - - "irc.freenode.org#haskell-lens" - skip_join: true - template: - - "\x0313linear\x03/\x0306%{branch}\x03 \x0314%{commit}\x03 %{build_url} %{message}" - -env: - - mode="--enable-tests" script="cabal test" diff --git a/CHANGELOG.markdown b/CHANGELOG.markdown --- a/CHANGELOG.markdown +++ b/CHANGELOG.markdown @@ -1,3 +1,420 @@ +1.23.3 [2026.01.10] +------------------- +* Remove unused `ghc-prim`, `tagged, `transformers-compat`, and `void` + dependencies. + +1.23.2 [2025.06.17] +------------------- +* Replace `test-framework` with `tasty` in the test suite. + +1.23.1 [2025.03.03] +------------------- +* Add `Uniform` and `UniformRange` instances for `Plucker`, `Quaternion`, `V`, + and `V{0,1,2,3,4}`. + +1.23 [2024.04.15] +----------------- +* The direction of interpolation of `lerp` has been reversed; + now `lerp 0 a b == a` and `lerp 1 a b == b`. + This brings `lerp` in line not only with its implementation + in other languages and frameworks, but also with `slerp` in this package. + +1.22 [2022.11.30] +----------------- +* The types of `_Point` and `lensP` have been generalized: + + ```diff + -_Point :: Iso' (Point f a) (f a) + +_Point :: Iso (Point f a) (Point g b) (f a) (g b) + + -lensP :: Lens' (Point g a) (g a) + +lensP :: Lens (Point f a) (Point g b) (f a) (g b) + ``` + + There is a chance that existing uses of `_Point` or `lensP` will fail to + typecheck due to their more general types. You can use `_Point.simple` or + `lensP.simple` to restore their old, more restricted types (where `simple` + comes from `Control.Lens` in the `lens` library). + +1.21.10 [2022.06.21] +-------------------- +* Allow building with `vector-0.13.*`. + +1.21.9 [2022.05.18] +------------------- +* Allow building with `transformers-0.6.*`. + +1.21.8 [2021.11.15] +------------------- +* Allow building with `hashable-1.4.*`. +* Drop support for pre-8.0 versions of GHC. + +1.21.7 [2021.09.20] +------------------- +* Fix a build error when using `random-1.2.1` or later. + +1.21.6 [2021.07.05] +------------------- +* Fix a build error when configured with `-template-haskell`. + +1.21.5 [2021.02.18] +------------------- +* Allow building with `lens-5.*`. + +1.21.4 [2021.01.29] +------------------- +* Allow building with `vector-0.12.2` or later. +* The build-type has been changed from `Custom` to `Simple`. + To achieve this, the `doctests` test suite has been removed in favor of using + [`cabal-docspec`](https://github.com/phadej/cabal-extras/tree/master/cabal-docspec) + to run the doctests. + +1.21.3 [2020.10.03] +------------------- +* Allow building with GHC 9.0. + +1.21.2 [2020.09.30] +------------------- +* Use `base-orphans-0.8.3` or later. This means that the `Linear.Instances` + module no longer defines any orphan instances of its own, and the module is + now a simple shim on top of `Data.Orphans` from `base-orphans`. + +1.21.1 [2020.06.25] +------------------- +* Allow building with `random-1.2.*`. + +1.21 [2020.02.03] +----------------- +* Add instances for direct sums (`Product`) and tensor products (`Compose`) of + other vector spaces. This makes is much more convenient to do things like treat + a matrix temporarily as a vector through Compose, or to consider things like + Gauss-Jordan elimination, which wants augmented structures. +* Add `frobenius` for computing the Frobenius norm of a matrix. +* Added `Random` instances for `System.Random`. We had an indirect dependency + through `vector` anyways. +* Add "obvious" zipping `Semigroup` and `Monoid` instances to all the + representable vector spaces. +* Add `R1`..`R4` instances to `Quaternion`. `_w` is the scalar component so that + `_x`,`_y`,`_z` can be directional. +* Add more solvers to `Linear.Matrix`, available with `base-4.8` or later. +* Add `unangle` function to `Linear.V2`. + +1.20.9 [2019.05.02] +------------------- +* Derive `Lift` instances for `Plucker`, `Quaternion`, and `V{0,1,2,3,4}`. + +1.20.8 [2018.07.03] +------------------- +* Add instances of the `Field` classes from `lens`. +* Add `Epsilon` instance for `Complex`. +* Use specialized implementations of the `null` and `length` methods in + `Foldable` instances. +* Add `Hashable1` instances for data types in `linear`. Also add a + `Hashable` instance for `V`. +* Fix a bug in which `Quaternion`s were incorrectly exponentiated. + +1.20.7 +------ +* Support `semigroupoids-5.2.1` and `doctest-0.12` + +1.20.6 +------ +* Revamp `Setup.hs` to use `cabal-doctest`. This makes it build + with `Cabal-2.0`, and makes the `doctest`s work with `cabal new-build` and + sandboxes. +* Make `(1 / x)` and `recip x` agree in the `Fractional` instance for `Quaternion` +* Use newtype instances for `Point` vectors in `Linear.Affine` +* Enable `PolyKinds` in `Linear.Trace`. Also enable `PolyKinds` when GHC 7.6 or + later is used (previously, it was GHC 7.8 or later). +* Fix a segfault arising from the `MVector` instance for `V` +* Add `Finite` class for conversion between `V` and fixed-size vector types + +1.20.5 +------ +* GHC 8 compatibility +* Fixed the `perspective` calculation. + +1.20.4 +------ +* Compatibility with `base-orphans` 0.5 + +1.20.3 +------ +* Support `vector` 0.11.0.0. +* Support `cereal` 0.5 +* You can now unboxed vectors of `V n` vectors. + +1.20.2 +------ +* Modified the `doctest` machinery to work with `stack` and builds to non-standard locations. +* Removed the local `.ghci` file. +* Various numerical stability improvements were made to the quaternion and projection functions. + +1.20.1 +------ +* Fixed doctests broken by the previous change. +* Unboxed vector instances for various linear data types now use unpacked integers even on older GHCs. + +1.20 +---- +* `inv22`, `inv33` and `inv44` no longer attempt an epsilon check. They no longer return a `Maybe` result as a consequence. + You should filter for the 0 determinant case yourself. + +1.19.1.3 +-------- +* `vector` 0.11.0.0 support + +1.19.1.2 +-------- +* Fix GHC 7.4. + +1.19.1.1 +-------- +* Proper `reflection` 2 support + +1.19.1 +------ +* `reflection` 2 support + +1.19 +---- +* Change the Ixed instance for `Linear.V` to use `Int` as the index type. This makes `V n` a _lot_ easier to use. + +1.18.3 +------ +* Compile warning-free on GHC 7.10. + + +1.18.2 +------ +* Added `NFData` instance for `Point` + +1.18.1 +------ +* Added an `-f-template-haskell` option to allow disabling `template-haskell` support. This is an unsupported configuration but may be useful for expert users in sandbox configurations. +* Added lenses for extracting corner various sub-matrices e.g. `_m22`, `_m33` + +1.18.0.2 +-------- +* Fixed builds on even older GHCs. + +1.18.0.1 +-------- +* Fixed the test suite. +* Fixed builds on older GHCs. + +1.18 +---- +* Consolidated `eye2` .. `eye4` into a single `identity` combinator. +* Fixed the `Data` instance `V n a` for GHC 7.10-RC3. + +1.17.1.1 +-------- +* `filepath` 1.4 support + +1.17.1 +------ +* Added support for `Data.Functor.Classes` from `transformers` 0.5 via `transformers-compat`. +* Added missing support for `binary`, `bytes` and `cereal` for `Point` + +1.17 +---- +* Better support for `binary`. Added support for `bytes` and `cereal` + +1.16.4 +------ +* `ortho` and `inverseOrtho` now only require a `Fractional` constraint. +* Added missing `Floating` instances. + +1.16.3 +---- +* Improve the performance of `fromQuaternion`, `mkTransformation`, + `mkTransformationMat`, `basisFor`, `scaled` by using implementations + that inline well for functions that were previously reference + implementations. + +1.16.2 +---- +* Added `NFData` instances for the various vector types. +* Added `!!/` operator for matrix division by scalar. + +1.16.1 +---- +* Added `Trace` instance for `V1`. + +1.16 +---- +* Renamed `kronecker` to `scaled`. + +1.15.5 +------ +* Added `Metric` instances for `[]`, `ZipList`, `Maybe` +* Added `det44` and `inv44` to `Linear.Matrix` +* Added `Data` instance for `Point` + +1.15.4 +------ +* Added Typeable and Data instances for V + +1.15.3 +------ +* Added missing `FunctorWithIndex`, `FoldableWithIndex` and `TraversableWithIndex Int (V n)` instances for `V` + +1.15.2 +------ +* Added `frustum`, analogous to the old `glFrustum` call. +* Added `inverseInfinitePerspective`, `inverseOrtho`, `inverseFrustum`. + +1.15.1 +------ +* Added `inversePerspective`. It is much more accurate to compute it directly than to compute an inverse. + +1.15.0.1 +-------- +* Fixed build failures caused by `Linear` re-exporting the old name. + +1.15 +---- +* Renamed `Linear.Perspective` to `Linear.Projection`. +* Fixed a build issue with GHC HEAD. + +1.14.0.1 +-------- +* Fixed test failures caused by 1.14 + +1.14 +---- +* Moved `Coincides` to `Linear.Plucker.Coincides`. The constructors `Line` and `Ray` oft collided with user code. + +1.13 +---- +* Switched 'ortho' to follow the OpenGL handedness. + +1.12.1 +------ +* Added "swizzle" lenses **e.g.** `_yzx`, which are useful for working with libraries like `gl`. + +1.12 +------ +* Added 'transpose' +* Added missing 'Mxy' matrices up to 4 dimensions -- they were commonly reimplemented by users. + +1.11.3 +------ +* Fixed an issue with `UndecidableInstances` on GHC 7.6.3 + +1.11.2 +------ +* Added `Linear.Perspective`. + +1.11.1 +------ +* Added `_Point`, `relative` and a few instances for `Point`. + +1.11 +---- +* Changed the 'representation' of `V n` from `E (V n)`, which was hard to use, to `Int`, which is a bit too permissive, but is easy to use. + +1.10.1 +------ +* Added `Linear.V2.angle`. + +1.10 +---- +* Added `Hashable` instances. + +1.9.1 +----- +* Added a role annotation to `V n a` to prevent users from using GHC 7.8's `Coercible` machinery to violate invariants. + +1.9.0.1 +----- +* Fixed a broken build + +1.9 +--- +* Added `MonadZip` instances. +* Added `MonadFix` instances. +* Added `Control.Lens.Each.Each` instances + +1.8.1 +----- +* Bugfixed `slerp` + +1.8 +--- +* Added missing `Unbox` instances for working with unboxed vectors of `linear` data types. + +1.7 +--- +* Fixed `axisAngle` +* `unit` now has a rank 1 type. + +1.5 +--- +* `lens` 4 compatibility + +1.4 +--- +* Renamed `incore` to `column` and added an example. + +1.3.1.1 +------- +* Build bugfix + +1.3.1 +--- +* Better implementations of `basis` and `basisFor`. +* Derived Generic instances. + +1.2 +--- +* Improved matrix multiplication to properly support the sparse/sparse case. + +1.1.4 +----- +* Marked modules `Trustworthy` as necessary. + +1.1.2 +----- +* Dependency bump for `reflection` compatibility + +1.1.1 +----- +* Fixed an infinite loop in the default definition of `liftI2`. + +1.1 +--- +* Added `Additive` instances for `[]`, `Maybe` and `Vector`. + +1.0 +--- +* Strict vectors +* Exported `mkTransformationMat` +* Bumped dependency bounds + +0.9.1 [bug fix] +----- +* Exported `Linear.V0`! + +0.9 +--- +* Added sparse vector support. + +0.8 +--- +* Added `Linear.V0` + +0.7 +--- +* Added `Linear.Instances` +* More documentation + +0.6 +--- +* Removed the direct dependency on `lens`. +* Added `Linear.Core` to cover vector spaces as corepresentable functors. + 0.5 ------- * Added `Ix` instances for `V2`, `V3`, and `V4` diff --git a/LICENSE b/LICENSE --- a/LICENSE +++ b/LICENSE @@ -1,4 +1,4 @@ -Copyright 2011-13 Edward Kmett +Copyright 2011-2015 Edward Kmett All rights reserved. diff --git a/README.markdown b/README.markdown --- a/README.markdown +++ b/README.markdown @@ -1,6 +1,8 @@ linear ====== +[![Hackage](https://img.shields.io/hackage/v/linear.svg)](https://hackage.haskell.org/package/linear) [![Build Status](https://github.com/ekmett/linear/workflows/Haskell-CI/badge.svg)](https://github.com/ekmett/linear/actions?query=workflow%3AHaskell-CI) + Highly polymorphic vector space operations on sparse and free vector spaces. Contact Information diff --git a/Setup.lhs b/Setup.lhs --- a/Setup.lhs +++ b/Setup.lhs @@ -1,44 +1,7 @@ #!/usr/bin/runhaskell -\begin{code} -{-# OPTIONS_GHC -Wall #-} -module Main (main) where - -import Data.List ( nub ) -import Data.Version ( showVersion ) -import Distribution.Package ( PackageName(PackageName), PackageId, InstalledPackageId, packageVersion, packageName ) -import Distribution.PackageDescription ( PackageDescription(), TestSuite(..) ) -import Distribution.Simple ( defaultMainWithHooks, UserHooks(..), simpleUserHooks ) -import Distribution.Simple.Utils ( rewriteFile, createDirectoryIfMissingVerbose ) -import Distribution.Simple.BuildPaths ( autogenModulesDir ) -import Distribution.Simple.Setup ( BuildFlags(buildVerbosity), fromFlag ) -import Distribution.Simple.LocalBuildInfo ( withLibLBI, withTestLBI, LocalBuildInfo(), ComponentLocalBuildInfo(componentPackageDeps) ) -import Distribution.Verbosity ( Verbosity ) -import System.FilePath ( () ) - -main :: IO () -main = defaultMainWithHooks simpleUserHooks - { buildHook = \pkg lbi hooks flags -> do - generateBuildModule (fromFlag (buildVerbosity flags)) pkg lbi - buildHook simpleUserHooks pkg lbi hooks flags - } - -generateBuildModule :: Verbosity -> PackageDescription -> LocalBuildInfo -> IO () -generateBuildModule verbosity pkg lbi = do - let dir = autogenModulesDir lbi - createDirectoryIfMissingVerbose verbosity True dir - withLibLBI pkg lbi $ \_ libcfg -> do - withTestLBI pkg lbi $ \suite suitecfg -> do - rewriteFile (dir "Build_" ++ testName suite ++ ".hs") $ unlines - [ "module Build_" ++ testName suite ++ " where" - , "deps :: [String]" - , "deps = " ++ (show $ formatdeps (testDeps libcfg suitecfg)) - ] - where - formatdeps = map (formatone . snd) - formatone p = case packageName p of - PackageName n -> n ++ "-" ++ showVersion (packageVersion p) +> module Main (main) where -testDeps :: ComponentLocalBuildInfo -> ComponentLocalBuildInfo -> [(InstalledPackageId, PackageId)] -testDeps xs ys = nub $ componentPackageDeps xs ++ componentPackageDeps ys +> import Distribution.Simple -\end{code} +> main :: IO () +> main = defaultMain diff --git a/linear.cabal b/linear.cabal --- a/linear.cabal +++ b/linear.cabal @@ -1,75 +1,149 @@ name: linear category: Math, Algebra -version: 0.9.2 +version: 1.23.3 license: BSD3 -cabal-version: >= 1.8 +cabal-version: >= 1.10 license-file: LICENSE author: Edward A. Kmett maintainer: Edward A. Kmett stability: provisional homepage: http://github.com/ekmett/linear/ bug-reports: http://github.com/ekmett/linear/issues -copyright: Copyright (C) 2012-2013 Edward A. Kmett +copyright: Copyright (C) 2012-2015 Edward A. Kmett synopsis: Linear Algebra description: Types and combinators for linear algebra on free vector spaces -build-type: Custom -tested-with: GHC == 7.4.1, GHC == 7.4.2, GHC == 7.6.1 +build-type: Simple +tested-with: GHC == 8.0.2 + , GHC == 8.2.2 + , GHC == 8.4.4 + , GHC == 8.6.5 + , GHC == 8.8.4 + , GHC == 8.10.7 + , GHC == 9.0.2 + , GHC == 9.2.8 + , GHC == 9.4.8 + , GHC == 9.6.7 + , GHC == 9.8.4 + , GHC == 9.10.3 + , GHC == 9.12.2 + , GHC == 9.14.1 extra-source-files: - .ghci .gitignore - .travis.yml + .hlint.yaml .vim.custom - travis/cabal-apt-install - travis/config CHANGELOG.markdown README.markdown +flag template-haskell + description: + You can disable the use of the `template-haskell` package using `-f-template-haskell`. + . + Disabling this is an unsupported configuration, but it may be useful for accelerating builds in sandboxes for expert users. + default: True + manual: True + +flag herbie + description: Enable `herbie`. + default: False + manual: True + source-repository head type: git - location: git://github.com/ekmett/linear.git + location: https://github.com/ekmett/linear library build-depends: - base >= 4.5 && < 5, - containers >= 0.4 && < 0.6, - distributive >= 0.2.2, - hashable >= 1.1 && < 1.3, - semigroups >= 0.9, - semigroupoids >= 3, - transformers >= 0.2 && < 0.4, - unordered-containers >= 0.2.3 + adjunctions >= 4 && < 5, + base >= 4.9 && < 5, + base-orphans >= 0.8.3 && < 1, + binary >= 0.5 && < 0.9, + bytes >= 0.15 && < 1, + cereal >= 0.4.1.1 && < 0.6, + containers >= 0.4 && < 0.9, + deepseq >= 1.1 && < 1.6, + distributive >= 0.5.1 && < 1, + hashable >= 1.2.7.0 && < 1.6, + indexed-traversable >= 0.1.1 && < 0.2, + lens >= 4.15.2 && < 6, + random >= 1.2 && < 1.4, + reflection >= 2 && < 3, + semigroupoids >= 5.2.1 && < 7, + transformers >= 0.5 && < 0.7, + unordered-containers >= 0.2.3 && < 0.3, + vector >= 0.12.1.2 && < 0.14 + if flag(template-haskell) && impl(ghc) + build-depends: template-haskell >= 2.11.1.0 && < 3.0 + + if flag(herbie) + build-depends: HerbiePlugin >= 0.1 && < 0.2 + ghc-options: -fplugin=Herbie + cpp-options: -DHERBIE + exposed-modules: Linear + Linear.Affine + Linear.Algebra + Linear.Binary Linear.Conjugate - Linear.Core + Linear.Covector Linear.Epsilon Linear.Instances Linear.Matrix Linear.Metric Linear.Plucker + Linear.Plucker.Coincides + Linear.Projection Linear.Quaternion + Linear.Trace + Linear.V Linear.V0 + Linear.V1 Linear.V2 Linear.V3 Linear.V4 Linear.Vector - ghc-options: -Wall -fwarn-tabs -O2 -fdicts-cheap -funbox-strict-fields + ghc-options: -Wall -Wtabs -O2 -fdicts-cheap -funbox-strict-fields -Wno-trustworthy-safe hs-source-dirs: src --- Verify the results of the examples + default-language: Haskell2010 + + x-docspec-extra-packages: simple-reflect + +-- We need this dummy test-suite to add simple-reflect to the install plan +-- +-- When cabal-install's extra-packages support becomes widely available +-- (i.e. after 3.4 release), we can remove this test-suite. test-suite doctests - type: exitcode-stdio-1.0 - main-is: doctests.hs - build-depends: - base, - directory >= 1.0 && < 1.3, - doctest >= 0.8 && < 0.10, - filepath >= 1.3 && < 1.4, - lens >= 3.7, - simple-reflect >= 0.3.1 + type: exitcode-stdio-1.0 + main-is: doctests.hs + hs-source-dirs: tests + default-language: Haskell2010 - ghc-options: -Wall -Werror -threaded + build-depends: base < 5, simple-reflect >= 0.3.1 + +test-suite test + type: exitcode-stdio-1.0 + main-is: Test.hs + other-modules: Prop.Quaternion + Prop.V3 + Unit.Binary + Unit.Plucker + Unit.V + ghc-options: -Wall -threaded hs-source-dirs: tests + build-depends: + base, + binary, + bytestring, + deepseq, + tasty >= 1.4 && < 1.6, + tasty-hunit >= 0.10 && < 0.11, + tasty-quickcheck >= 0.10 && < 0.12, + linear, + QuickCheck >= 2.5, + reflection, + vector + default-language: Haskell2010 diff --git a/src/Linear.hs b/src/Linear.hs --- a/src/Linear.hs +++ b/src/Linear.hs @@ -1,7 +1,6 @@ ----------------------------------------------------------------------------- -- | --- Module : Linear --- Copyright : (C) 2012-2013 Edward Kmett, +-- Copyright : (C) 2012-2015 Edward Kmett -- License : BSD-style (see the file LICENSE) -- -- Maintainer : Edward Kmett @@ -12,32 +11,38 @@ -- that make up the linear package. ---------------------------------------------------------------------------- module Linear - ( module Linear.Conjugate - , module Linear.Core + ( module Linear.Algebra + , module Linear.Binary + , module Linear.Conjugate + , module Linear.Covector , module Linear.Epsilon , module Linear.Matrix , module Linear.Metric - , module Linear.Plucker + , module Linear.Projection , module Linear.Quaternion + , module Linear.Trace , module Linear.V0 + , module Linear.V1 , module Linear.V2 , module Linear.V3 , module Linear.V4 , module Linear.Vector ) where +import Linear.Algebra +import Linear.Binary import Linear.Conjugate -import Linear.Core +import Linear.Covector import Linear.Epsilon import Linear.Instances () import Linear.Matrix import Linear.Metric -import Linear.Plucker +import Linear.Projection import Linear.Quaternion +import Linear.Trace import Linear.V0 +import Linear.V1 import Linear.V2 import Linear.V3 import Linear.V4 import Linear.Vector - -{-# ANN module "Hlint: ignore Use import/export shortcut" #-} diff --git a/src/Linear/Affine.hs b/src/Linear/Affine.hs new file mode 100644 --- /dev/null +++ b/src/Linear/Affine.hs @@ -0,0 +1,303 @@ +{-# LANGUAGE CPP #-} +{-# LANGUAGE FlexibleContexts #-} +{-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE GeneralizedNewtypeDeriving #-} +{-# LANGUAGE DeriveTraversable #-} +{-# LANGUAGE MultiParamTypeClasses #-} +{-# LANGUAGE UndecidableInstances #-} +{-# LANGUAGE TypeFamilies #-} +{-# LANGUAGE TypeOperators #-} +{-# LANGUAGE RankNTypes #-} +{-# LANGUAGE Trustworthy #-} +{-# LANGUAGE DeriveGeneric #-} +{-# LANGUAGE DeriveDataTypeable #-} +{-# LANGUAGE StandaloneDeriving #-} +{-# LANGUAGE ScopedTypeVariables #-} + +----------------------------------------------------------------------------- +-- | +-- License : BSD-style (see the file LICENSE) +-- Maintainer : Edward Kmett +-- Stability : provisional +-- Portability : portable +-- +-- Operations on affine spaces. +----------------------------------------------------------------------------- +module Linear.Affine where + +import Control.Applicative +import Control.DeepSeq +import Control.Monad (liftM) +import Control.Lens +import Data.Binary as Binary +import Data.Bytes.Serial +import Data.Coerce +import Data.Complex (Complex) +import Data.Data +import Data.Distributive +import Data.Foldable as Foldable +import Data.Functor.Bind +import Data.Functor.Classes +import Data.Functor.Product +import Data.Functor.Rep as Rep +import Data.HashMap.Lazy (HashMap) +import Data.Hashable +import Data.Hashable.Lifted +import Data.IntMap (IntMap) +import Data.Ix +import Data.Kind +import Data.Map (Map) +#if !(MIN_VERSION_base(4,11,0)) +import Data.Semigroup (Semigroup) +#endif +import Data.Serialize as Cereal +import Data.Vector (Vector) +import qualified Data.Vector.Generic.Mutable as M +import qualified Data.Vector.Generic as G +import qualified Data.Vector.Unboxed.Base as U +import Foreign.Storable +import GHC.Generics (Generic, Generic1) +import Linear.Epsilon +import Linear.Metric +import Linear.Plucker +import Linear.Quaternion +import Linear.V +import Linear.V0 +import Linear.V1 +import Linear.V2 +import Linear.V3 +import Linear.V4 +import Linear.Vector +import System.Random (Random(..)) + +-- | An affine space is roughly a vector space in which we have +-- forgotten or at least pretend to have forgotten the origin. +-- +-- > a .+^ (b .-. a) = b@ +-- > (a .+^ u) .+^ v = a .+^ (u ^+^ v)@ +-- > (a .-. b) ^+^ v = (a .+^ v) .-. q@ +class Additive (Diff p) => Affine p where + type Diff p :: Type -> Type + + infixl 6 .-. + -- | Get the difference between two points as a vector offset. + (.-.) :: Num a => p a -> p a -> Diff p a + + infixl 6 .+^ + -- | Add a vector offset to a point. + (.+^) :: Num a => p a -> Diff p a -> p a + + infixl 6 .-^ + -- | Subtract a vector offset from a point. + (.-^) :: Num a => p a -> Diff p a -> p a + p .-^ v = p .+^ negated v + {-# INLINE (.-^) #-} + +instance (Affine f, Affine g) => Affine (Product f g) where + type Diff (Product f g) = Product (Diff f) (Diff g) + Pair a b .-. Pair c d = Pair (a .-. c) (b .-. d) + Pair a b .+^ Pair c d = Pair (a .+^ c) (b .+^ d) + Pair a b .-^ Pair c d = Pair (a .+^ c) (b .+^ d) + +-- | Compute the quadrance of the difference (the square of the distance) +qdA :: (Affine p, Foldable (Diff p), Num a) => p a -> p a -> a +qdA a b = Foldable.sum (fmap (join (*)) (a .-. b)) +{-# INLINE qdA #-} + +-- | Distance between two points in an affine space +distanceA :: (Floating a, Foldable (Diff p), Affine p) => p a -> p a -> a +distanceA a b = sqrt (qdA a b) +{-# INLINE distanceA #-} + +#define ADDITIVEC(CTX,T) instance CTX => Affine T where type Diff T = T ; \ + (.-.) = (^-^) ; {-# INLINE (.-.) #-} ; (.+^) = (^+^) ; {-# INLINE (.+^) #-} ; \ + (.-^) = (^-^) ; {-# INLINE (.-^) #-} +#define ADDITIVE(T) ADDITIVEC((), T) + +ADDITIVE([]) +ADDITIVE(Complex) +ADDITIVE(ZipList) +ADDITIVE(Maybe) +ADDITIVE(IntMap) +ADDITIVE(Identity) +ADDITIVE(Vector) +ADDITIVE(V0) +ADDITIVE(V1) +ADDITIVE(V2) +ADDITIVE(V3) +ADDITIVE(V4) +ADDITIVE(Plucker) +ADDITIVE(Quaternion) +ADDITIVE(((->) b)) +ADDITIVEC(Ord k, (Map k)) +ADDITIVEC((Eq k, Hashable k), (HashMap k)) +ADDITIVEC(Dim n, (V n)) + +-- | A handy wrapper to help distinguish points from vectors at the +-- type level +newtype Point f a = P (f a) + deriving ( Eq, Ord, Show, Read, Monad, Functor, Applicative, Foldable + , Eq1, Ord1, Show1, Read1 + , Traversable, Apply, Additive, Metric + , Fractional , Num, Ix, Storable, Epsilon + , Semigroup, Monoid + , Random, Hashable + , Generic, Generic1, Data + ) + +instance Finite f => Finite (Point f) where + type Size (Point f) = Size f + toV (P v) = toV v + fromV v = P (fromV v) + +instance NFData (f a) => NFData (Point f a) where + rnf (P x) = rnf x + +instance Serial1 f => Serial1 (Point f) where + serializeWith f (P p) = serializeWith f p + deserializeWith m = P `liftM` deserializeWith m + +instance Serial (f a) => Serial (Point f a) where + serialize (P p) = serialize p + deserialize = P `liftM` deserialize + +instance Binary (f a) => Binary (Point f a) where + put (P p) = Binary.put p + get = P `liftM` Binary.get + +instance Serialize (f a) => Serialize (Point f a) where + put (P p) = Cereal.put p + get = P `liftM` Cereal.get + +instance Hashable1 f => Hashable1 (Point f) where + liftHashWithSalt h s (P f) = liftHashWithSalt h s f + {-# INLINE liftHashWithSalt #-} + +lensP :: Lens (Point f a) (Point g b) (f a) (g b) +lensP afb (P a) = P <$> afb a +{-# INLINE lensP #-} + +_Point :: Iso (Point f a) (Point g b) (f a) (g b) +_Point = iso (\(P a) -> a) P +{-# INLINE _Point #-} + +instance (t ~ Point g b) => Rewrapped (Point f a) t +instance Wrapped (Point f a) where + type Unwrapped (Point f a) = f a + _Wrapped' = _Point + {-# INLINE _Wrapped' #-} + +-- These are stolen from Data.Profunctor.Unsafe +(.#) :: Coercible b a => (b -> c) -> (a -> b) -> a -> c +f .# _ = coerce f +{-# INLINE (.#) #-} + +(#.) :: Coercible c b => (b -> c) -> (a -> b) -> a -> c +(#.) _ = coerce (\x -> x :: b) :: forall a b. Coercible b a => a -> b +{-# INLINE (#.) #-} + +unP :: Point f a -> f a +unP (P x) = x +{-# INLINE unP #-} + +-- We can't use GND to derive 'Bind' because 'join' causes +-- role troubles. However, GHC 7.8 and above let us use +-- explicit coercions for (>>-). +instance Bind f => Bind (Point f) where + (>>-) = ((P .) . (. (unP .))) #. (>>-) .# unP + join (P m) = P $ m >>- \(P m') -> m' + +instance Distributive f => Distributive (Point f) where + distribute = P . collect (\(P p) -> p) + collect = (P .) #. collect .# (unP .) + +instance Representable f => Representable (Point f) where + type Rep (Point f) = Rep f + tabulate = P #. tabulate + {-# INLINE tabulate #-} + index = Rep.index .# unP + {-# INLINE index #-} + +type instance Index (Point f a) = Index (f a) +type instance IxValue (Point f a) = IxValue (f a) + +instance Ixed (f a) => Ixed (Point f a) where + ix l = lensP . ix l + {-# INLINE ix #-} + +instance Traversable f => Each (Point f a) (Point f b) a b where + each = traverse + {-# INLINE each #-} + +instance R1 f => R1 (Point f) where + _x = lensP . _x + {-# INLINE _x #-} + +instance R2 f => R2 (Point f) where + _y = lensP . _y + {-# INLINE _y #-} + _xy = lensP . _xy + {-# INLINE _xy #-} + +instance R3 f => R3 (Point f) where + _z = lensP . _z + {-# INLINE _z #-} + _xyz = lensP . _xyz + {-# INLINE _xyz #-} + +instance R4 f => R4 (Point f) where + _w = lensP . _w + {-# INLINE _w #-} + _xyzw = lensP . _xyzw + {-# INLINE _xyzw #-} + +instance Additive f => Affine (Point f) where + type Diff (Point f) = f + (.-.) = (. unP) #. (^-^) .# unP + {-# INLINE (.-.) #-} + (.+^) = (P .) #. (^+^) .# unP + {-# INLINE (.+^) #-} + (.-^) = (P .) #. (^-^) .# unP + {-# INLINE (.-^) #-} + +-- | Vector spaces have origins. +origin :: (Additive f, Num a) => Point f a +origin = P zero + +-- | An isomorphism between points and vectors, given a reference +-- point. +relative :: (Additive f, Num a) => Point f a -> Iso' (Point f a) (f a) +relative p0 = iso (.-. p0) (p0 .+^) +{-# INLINE relative #-} + +newtype instance U.Vector (Point f a) = V_P (U.Vector (f a)) +newtype instance U.MVector s (Point f a) = MV_P (U.MVector s (f a)) +instance U.Unbox (f a) => U.Unbox (Point f a) + +instance U.Unbox (f a) => M.MVector U.MVector (Point f a) where + {-# INLINE basicLength #-} + {-# INLINE basicUnsafeSlice #-} + {-# INLINE basicOverlaps #-} + {-# INLINE basicUnsafeNew #-} + {-# INLINE basicUnsafeRead #-} + {-# INLINE basicUnsafeWrite #-} + basicLength (MV_P v) = M.basicLength v + basicUnsafeSlice m n (MV_P v) = MV_P (M.basicUnsafeSlice m n v) + basicOverlaps (MV_P v) (MV_P u) = M.basicOverlaps v u + basicUnsafeNew n = MV_P `liftM` M.basicUnsafeNew n + basicUnsafeRead (MV_P v) i = P `liftM` M.basicUnsafeRead v i + basicUnsafeWrite (MV_P v) i (P x) = M.basicUnsafeWrite v i x + basicInitialize (MV_P v) = M.basicInitialize v + {-# INLINE basicInitialize #-} + +instance U.Unbox (f a) => G.Vector U.Vector (Point f a) where + {-# INLINE basicUnsafeFreeze #-} + {-# INLINE basicUnsafeThaw #-} + {-# INLINE basicLength #-} + {-# INLINE basicUnsafeSlice #-} + {-# INLINE basicUnsafeIndexM #-} + basicUnsafeFreeze (MV_P v) = V_P `liftM` G.basicUnsafeFreeze v + basicUnsafeThaw ( V_P v) = MV_P `liftM` G.basicUnsafeThaw v + basicLength ( V_P v) = G.basicLength v + basicUnsafeSlice m n (V_P v) = V_P (G.basicUnsafeSlice m n v) + basicUnsafeIndexM (V_P v) i = P `liftM` G.basicUnsafeIndexM v i diff --git a/src/Linear/Algebra.hs b/src/Linear/Algebra.hs new file mode 100644 --- /dev/null +++ b/src/Linear/Algebra.hs @@ -0,0 +1,136 @@ +{-# LANGUAGE CPP #-} +{-# LANGUAGE MultiParamTypeClasses #-} +{-# LANGUAGE FlexibleContexts #-} +{-# LANGUAGE FlexibleInstances #-} +----------------------------------------------------------------------------- +-- | +-- License : BSD-style (see the file LICENSE) +-- Maintainer : Edward Kmett +-- Stability : provisional +-- Portability : portable +-- +----------------------------------------------------------------------------- +module Linear.Algebra + ( Algebra(..) + , Coalgebra(..) + , multRep, unitalRep + , comultRep, counitalRep + ) where + +import Control.Lens hiding (index) +import Data.Functor.Rep +import Data.Complex +import Data.Void +import Linear.Vector +import Linear.Quaternion +import Linear.Conjugate +import Linear.V0 +import Linear.V1 +import Linear.V2 +import Linear.V3 +import Linear.V4 + +-- | An associative unital algebra over a ring +class Num r => Algebra r m where + mult :: (m -> m -> r) -> m -> r + unital :: r -> m -> r + +multRep :: (Representable f, Algebra r (Rep f)) => f (f r) -> f r +multRep ffr = tabulate $ mult (index . index ffr) + +unitalRep :: (Representable f, Algebra r (Rep f)) => r -> f r +unitalRep = tabulate . unital + +instance Num r => Algebra r Void where + mult _ _ = 0 + unital _ _ = 0 + +instance Num r => Algebra r (E V0) where + mult _ _ = 0 + unital _ _ = 0 + +instance Num r => Algebra r (E V1) where + mult f _ = f ex ex + unital r _ = r + +instance Num r => Algebra r () where + mult f () = f () () + unital r () = r + +instance (Algebra r a, Algebra r b) => Algebra r (a, b) where + mult f (a,b) = mult (\a1 a2 -> mult (\b1 b2 -> f (a1,b1) (a2,b2)) b) a + unital r (a,b) = unital r a * unital r b + +instance Num r => Algebra r (E Complex) where + mult f = \ i -> c^.el i where + c = (f ee ee - f ei ei) :+ (f ee ei + f ei ee) + unital r i = (r :+ 0)^.el i + +instance (Num r, TrivialConjugate r) => Algebra r (E Quaternion) where + mult f = index $ Quaternion + (f ee ee - (f ei ei + f ej ej + f ek ek)) + (V3 (f ee ei + f ei ee + f ej ek - f ek ej) + (f ee ej + f ej ee + f ek ei - f ei ek) + (f ee ek + f ek ee + f ei ej - f ej ei)) + unital r = index (Quaternion r 0) + +-- | A coassociative counital coalgebra over a ring +class Num r => Coalgebra r m where + comult :: (m -> r) -> m -> m -> r + counital :: (m -> r) -> r + +comultRep :: (Representable f, Coalgebra r (Rep f)) => f r -> f (f r) +comultRep fr = tabulate $ \i -> tabulate $ \j -> comult (index fr) i j + +counitalRep :: (Representable f, Coalgebra r (Rep f)) => f r -> r +counitalRep = counital . index + +instance Num r => Coalgebra r Void where + comult _ _ _ = 0 + counital _ = 0 + +instance Num r => Coalgebra r () where + comult f () () = f () + counital f = f () + +instance Num r => Coalgebra r (E V0) where + comult _ _ _ = 0 + counital _ = 0 + +instance Num r => Coalgebra r (E V1) where + comult f _ _ = f ex + counital f = f ex + +instance Num r => Coalgebra r (E V2) where + comult f = index . index v where + v = V2 (V2 (f ex) 0) (V2 0 (f ey)) + counital f = f ex + f ey + +instance Num r => Coalgebra r (E V3) where + comult f = index . index q where + q = V3 (V3 (f ex) 0 0) + (V3 0 (f ey) 0) + (V3 0 0 (f ez)) + counital f = f ex + f ey + f ez + +instance Num r => Coalgebra r (E V4) where + comult f = index . index v where + v = V4 (V4 (f ex) 0 0 0) (V4 0 (f ey) 0 0) (V4 0 0 (f ez) 0) (V4 0 0 0 (f ew)) + counital f = f ex + f ey + f ez + f ew + +instance Num r => Coalgebra r (E Complex) where + comult f = \i j -> c^.el i.el j where + c = (f ee :+ 0) :+ (0 :+ f ei) + counital f = f ee + f ei + +instance (Num r, TrivialConjugate r) => Coalgebra r (E Quaternion) where + comult f = index . index + (Quaternion (Quaternion (f ee) (V3 0 0 0)) + (V3 (Quaternion 0 (V3 (f ei) 0 0)) + (Quaternion 0 (V3 0 (f ej) 0)) + (Quaternion 0 (V3 0 0 (f ek))))) + counital f = f ee + f ei + f ej + f ek + +instance (Coalgebra r m, Coalgebra r n) => Coalgebra r (m, n) where + comult f (a1, b1) (a2, b2) = comult (\a -> comult (\b -> f (a, b)) b1 b2) a1 a2 + counital k = counital $ \a -> counital $ \b -> k (a,b) diff --git a/src/Linear/Binary.hs b/src/Linear/Binary.hs new file mode 100644 --- /dev/null +++ b/src/Linear/Binary.hs @@ -0,0 +1,27 @@ +----------------------------------------------------------------------------- +-- | +-- Copyright : (C) 2013-2015 Edward Kmett and Anthony Cowley +-- License : BSD-style (see the file LICENSE) +-- +-- Maintainer : Edward Kmett +-- Stability : experimental +-- Portability : non-portable +-- +-- Serialization of statically-sized types with the "Data.Binary" +-- library. +------------------------------------------------------------------------------ +module Linear.Binary + ( putLinear + , getLinear + ) where + +import Data.Binary +import Data.Foldable (traverse_) + +-- | Serialize a linear type. +putLinear :: (Binary a, Foldable t) => t a -> Put +putLinear = traverse_ put + +-- | Deserialize a linear type. +getLinear :: (Binary a, Applicative t, Traversable t) => Get (t a) +getLinear = sequenceA $ pure get diff --git a/src/Linear/Conjugate.hs b/src/Linear/Conjugate.hs --- a/src/Linear/Conjugate.hs +++ b/src/Linear/Conjugate.hs @@ -1,7 +1,9 @@ +{-# LANGUAGE CPP #-} +{-# LANGUAGE DefaultSignatures #-} + ----------------------------------------------------------------------------- -- | --- Module : Linear.Conjugate --- Copyright : (C) 2012-2013 Edward Kmett, +-- Copyright : (C) 2012-2015 Edward Kmett -- License : BSD-style (see the file LICENSE) -- -- Maintainer : Edward Kmett @@ -12,12 +14,18 @@ ---------------------------------------------------------------------------- module Linear.Conjugate ( Conjugate(..) + , TrivialConjugate ) where import Data.Complex hiding (conjugate) import Data.Int import Data.Word +import Foreign.C.Types (CFloat, CDouble) +-- $setup +-- >>> import Data.Complex (Complex (..)) + + -- | An involutive ring class Num a => Conjugate a where -- | Conjugate a value. This defaults to the trivial involution. @@ -28,8 +36,18 @@ -- >>> conjugate 1 -- 1 conjugate :: a -> a +#ifndef HLINT + default conjugate :: TrivialConjugate a => a -> a conjugate = id +#endif +-- | Requires and provides a default definition such that +-- +-- @ +-- 'conjugate' = 'id' +-- @ +class Conjugate a => TrivialConjugate a + instance Conjugate Integer instance Conjugate Int instance Conjugate Int64 @@ -43,7 +61,26 @@ instance Conjugate Word8 instance Conjugate Double instance Conjugate Float +instance Conjugate CFloat +instance Conjugate CDouble + instance (Conjugate a, RealFloat a) => Conjugate (Complex a) where {-# SPECIALIZE instance Conjugate (Complex Float) #-} {-# SPECIALIZE instance Conjugate (Complex Double) #-} conjugate (a :+ b) = conjugate a :+ negate b + +instance TrivialConjugate Integer +instance TrivialConjugate Int +instance TrivialConjugate Int64 +instance TrivialConjugate Int32 +instance TrivialConjugate Int16 +instance TrivialConjugate Int8 +instance TrivialConjugate Word +instance TrivialConjugate Word64 +instance TrivialConjugate Word32 +instance TrivialConjugate Word16 +instance TrivialConjugate Word8 +instance TrivialConjugate Double +instance TrivialConjugate Float +instance TrivialConjugate CFloat +instance TrivialConjugate CDouble diff --git a/src/Linear/Core.hs b/src/Linear/Core.hs deleted file mode 100644 --- a/src/Linear/Core.hs +++ /dev/null @@ -1,25 +0,0 @@ -{-# LANGUAGE RankNTypes #-} ------------------------------------------------------------------------------ --- | --- Module : Linear.Core --- Copyright : (C) 2012-2013 Edward Kmett, --- License : BSD-style (see the file LICENSE) --- --- Maintainer : Edward Kmett --- Stability : experimental --- Portability : non-portable --- --- Corepresentable functors as vector spaces ----------------------------------------------------------------------------- -module Linear.Core - ( Core(..) - ) where - --- | --- A 'Functor' @f@ is corepresentable if it is isomorphic to @(x -> a)@ --- for some x. Nearly all such functors can be represented by choosing @x@ to be --- the set of lenses that are polymorphic in the contents of the 'Functor', --- that is to say @x = 'Rep' f@ is a valid choice of 'x' for (nearly) every --- 'Representable' 'Functor'. -class Functor f => Core f where - core :: ((forall g x. Functor g => (x -> g x) -> f x -> g (f x)) -> a) -> f a diff --git a/src/Linear/Covector.hs b/src/Linear/Covector.hs new file mode 100644 --- /dev/null +++ b/src/Linear/Covector.hs @@ -0,0 +1,73 @@ +{-# LANGUAGE CPP, MultiParamTypeClasses, FlexibleInstances, FlexibleContexts #-} +----------------------------------------------------------------------------- +-- | +-- License : BSD-style (see the file LICENSE) +-- Maintainer : Edward Kmett +-- Stability : provisional +-- Portability : portable +-- +-- Operations on affine spaces. +----------------------------------------------------------------------------- +module Linear.Covector + ( Covector(..) + , ($*) + ) where + +import Control.Applicative +import Control.Monad +import Data.Functor.Plus hiding (zero) +import qualified Data.Functor.Plus as Plus +import Data.Functor.Bind +import Data.Functor.Rep as Rep +import Linear.Algebra + +-- | Linear functionals from elements of an (infinite) free module to a scalar + +newtype Covector r a = Covector { runCovector :: (a -> r) -> r } + +infixr 0 $* + +($*) :: Representable f => Covector r (Rep f) -> f r -> r +Covector f $* m = f (Rep.index m) + +instance Functor (Covector r) where + fmap f (Covector m) = Covector $ \k -> m (k . f) + +instance Apply (Covector r) where + Covector mf <.> Covector ma = Covector $ \k -> mf $ \f -> ma (k . f) + +instance Applicative (Covector r) where + pure a = Covector $ \k -> k a + Covector mf <*> Covector ma = Covector $ \k -> mf $ \f -> ma $ k . f + +instance Bind (Covector r) where + Covector m >>- f = Covector $ \k -> m $ \a -> runCovector (f a) k + +instance Monad (Covector r) where +#if !(MIN_VERSION_base(4,11,0)) + return a = Covector $ \k -> k a +#endif + Covector m >>= f = Covector $ \k -> m $ \a -> runCovector (f a) k + +instance Num r => Alt (Covector r) where + Covector m Covector n = Covector $ \k -> m k + n k + +instance Num r => Plus (Covector r) where + zero = Covector (const 0) + +instance Num r => Alternative (Covector r) where + Covector m <|> Covector n = Covector $ \k -> m k + n k + empty = Covector (const 0) + +instance Num r => MonadPlus (Covector r) where + Covector m `mplus` Covector n = Covector $ \k -> m k + n k + mzero = Covector (const 0) + +instance Coalgebra r m => Num (Covector r m) where + Covector f + Covector g = Covector $ \k -> f k + g k + Covector f - Covector g = Covector $ \k -> f k - g k + Covector f * Covector g = Covector $ \k -> f $ \m -> g $ comult k m + negate (Covector f) = Covector $ \k -> negate (f k) + abs _ = error "Covector.abs: undefined" + signum _ = error "Covector.signum: undefined" + fromInteger n = Covector $ \ k -> fromInteger n * counital k diff --git a/src/Linear/Epsilon.hs b/src/Linear/Epsilon.hs --- a/src/Linear/Epsilon.hs +++ b/src/Linear/Epsilon.hs @@ -1,7 +1,6 @@ ----------------------------------------------------------------------------- -- | --- Module : Linear.Epsilon --- Copyright : (C) 2012 Edward Kmett +-- Copyright : (C) 2012-2015 Edward Kmett -- License : BSD-style (see the file LICENSE) -- Maintainer : Edward Kmett -- Stability : provisional @@ -12,6 +11,8 @@ module Linear.Epsilon ( Epsilon(..) ) where +import Data.Complex (Complex, magnitude) +import Foreign.C.Types (CFloat, CDouble) -- | Provides a fairly subjective test to see if a quantity is near zero. -- @@ -37,3 +38,14 @@ -- | @'abs' a '<=' 1e-12@ instance Epsilon Double where nearZero a = abs a <= 1e-12 + +-- | @'abs' a '<=' 1e-6@ +instance Epsilon CFloat where + nearZero a = abs a <= 1e-6 + +-- | @'abs' a '<=' 1e-12@ +instance Epsilon CDouble where + nearZero a = abs a <= 1e-12 + +instance (Epsilon a, RealFloat a) => Epsilon (Complex a) where + nearZero = nearZero . magnitude diff --git a/src/Linear/Instances.hs b/src/Linear/Instances.hs --- a/src/Linear/Instances.hs +++ b/src/Linear/Instances.hs @@ -1,77 +1,14 @@ -{-# OPTIONS_GHC -fno-warn-orphans #-} +{-# LANGUAGE Safe #-} ----------------------------------------------------------------------------- -- | --- Module : Linear.Instances --- Copyright : (C) 2012 Edward Kmett +-- Copyright : (C) 2012-2015 Edward Kmett -- License : BSD-style (see the file LICENSE) -- Maintainer : Edward Kmett -- Stability : provisional -- Portability : portable -- --- Orphans +-- Re-exports orphan instances for @Complex@ from the @base-orphans@ package. ----------------------------------------------------------------------------- module Linear.Instances () where -import Control.Applicative -import Data.Complex -import Data.Foldable -import Data.Functor.Bind -import Data.HashMap.Lazy as HashMap -import Data.Hashable -import Data.Semigroup -import Data.Semigroup.Foldable -import Data.Semigroup.Traversable -import Data.Traversable - -instance (Hashable k, Eq k) => Apply (HashMap k) where - (<.>) = HashMap.intersectionWith id - -instance (Hashable k, Eq k) => Bind (HashMap k) where - -- this is needlessly painful - m >>- f = HashMap.fromList $ do - (k, a) <- HashMap.toList m - case HashMap.lookup k (f a) of - Just b -> [(k,b)] - Nothing -> [] - -instance Functor Complex where - fmap f (a :+ b) = f a :+ f b - {-# INLINE fmap #-} - -instance Apply Complex where - (a :+ b) <.> (c :+ d) = a c :+ b d - -instance Applicative Complex where - pure a = a :+ a - (a :+ b) <*> (c :+ d) = a c :+ b d - -instance Bind Complex where - (a :+ b) >>- f = a' :+ b' where - a' :+ _ = f a - _ :+ b' = f b - {-# INLINE (>>-) #-} - -instance Monad Complex where - return a = a :+ a - {-# INLINE return #-} - - (a :+ b) >>= f = a' :+ b' where - a' :+ _ = f a - _ :+ b' = f b - {-# INLINE (>>=) #-} - -instance Foldable Complex where - foldMap f (a :+ b) = f a `mappend` f b - {-# INLINE foldMap #-} - -instance Traversable Complex where - traverse f (a :+ b) = (:+) <$> f a <*> f b - {-# INLINE traverse #-} - -instance Foldable1 Complex where - foldMap1 f (a :+ b) = f a <> f b - {-# INLINE foldMap1 #-} - -instance Traversable1 Complex where - traverse1 f (a :+ b) = (:+) <$> f a <.> f b - {-# INLINE traverse1 #-} +import Data.Orphans () diff --git a/src/Linear/Matrix.hs b/src/Linear/Matrix.hs --- a/src/Linear/Matrix.hs +++ b/src/Linear/Matrix.hs @@ -1,7 +1,14 @@ ------------------------------------------------------------------------------ +{-# LANGUAGE BangPatterns #-} +{-# LANGUAGE CPP #-} +{-# LANGUAGE RankNTypes #-} +{-# LANGUAGE ScopedTypeVariables #-} +{-# LANGUAGE Trustworthy #-} +{-# LANGUAGE TypeFamilies #-} +{-# LANGUAGE TypeOperators #-} + +--------------------------------------------------------------------------- -- | --- Module : Linear.Matrix --- Copyright : (C) 2012-2013 Edward Kmett, +-- Copyright : (C) 2012-2015 Edward Kmett -- License : BSD-style (see the file LICENSE) -- -- Maintainer : Edward Kmett @@ -9,67 +16,128 @@ -- Portability : non-portable -- -- Simple matrix operation for low-dimensional primitives. ----------------------------------------------------------------------------- +--------------------------------------------------------------------------- module Linear.Matrix - ( (!*!), (!*) , (*!), (!!*), (*!!) + ( (!*!), (!+!), (!-!), (!*), (*!), (!!*), (*!!), (!!/) + , column , adjoint - , M22, M33, M44, M43, m33_to_m44, m43_to_m44 - , det22, det33, inv22, inv33 - , eye3, eye4 - , trace + , M22, M23, M24, M32, M33, M34, M42, M43, M44 + , m33_to_m44, m43_to_m44 + , det22, det33, det44, inv22, inv33, inv44 + , identity + , Trace(..) , translation + , transpose , fromQuaternion , mkTransformation + , mkTransformationMat + , _m22, _m23, _m24 + , _m32, _m33, _m34 + , _m42, _m43, _m44 + , lu + , luFinite + , forwardSub + , forwardSubFinite + , backwardSub + , backwardSubFinite + , luSolve + , luSolveFinite + , luInv + , luInvFinite + , luDet + , luDetFinite ) where -import Control.Applicative -import Control.Monad (join) +import Control.Lens hiding (index) +import Control.Lens.Internal.Context import Data.Distributive import Data.Foldable as Foldable -import Data.Functor.Apply -import Linear.Epsilon -import Linear.Metric +import Data.Functor.Rep +import GHC.TypeLits import Linear.Quaternion +import Linear.V import Linear.V2 import Linear.V3 import Linear.V4 -import Linear.Vector ((*^)) +import Linear.Vector import Linear.Conjugate +import Linear.Trace -- $setup --- >>> import Data.Complex --- >>> import Data.IntMap +-- >>> import Control.Lens hiding (index) +-- >>> import Data.Complex (Complex (..)) +-- >>> import Linear.V2 +-- >>> import Linear.V3 +-- >>> import Linear.V +-- >>> import qualified Data.IntMap as IntMap -- >>> import Debug.SimpleReflect.Vars +-- | This is a generalization of 'Control.Lens.inside' to work over any corepresentable 'Functor'. +-- +-- @ +-- 'column' :: 'Representable' f => 'Lens' s t a b -> 'Lens' (f s) (f t) (f a) (f b) +-- @ +-- +-- In practice it is used to access a column of a matrix. +-- +-- >>> V2 (V3 1 2 3) (V3 4 5 6) ^._x +-- V3 1 2 3 +-- +-- >>> V2 (V3 1 2 3) (V3 4 5 6) ^.column _x +-- V2 1 4 +column :: Representable f => LensLike (Context a b) s t a b -> Lens (f s) (f t) (f a) (f b) +column l f es = o <$> f i where + go = l (Context id) + i = tabulate $ \ e -> ipos $ go (index es e) + o eb = tabulate $ \ e -> ipeek (index eb e) (go (index es e)) + infixl 7 !*! --- | Matrix product. This can compute mixed dense-dense, sparse-dense and sparse-sparse matrix products. +-- | Matrix product. This can compute any combination of sparse and dense multiplication. -- -- >>> V2 (V3 1 2 3) (V3 4 5 6) !*! V3 (V2 1 2) (V2 3 4) (V2 4 5) -- V2 (V2 19 25) (V2 43 58) -- --- >>> V2 (fromList [(1,2)]) (fromList [(2,3)]) !*! fromList [(1,V3 0 0 1), (2, V3 0 0 5)] +-- >>> V2 (IntMap.fromList [(1,2)]) (IntMap.fromList [(2,3)]) !*! IntMap.fromList [(1,V3 0 0 1), (2, V3 0 0 5)] -- V2 (V3 0 0 2) (V3 0 0 15) -(!*!) :: (Functor m, Foldable r, Apply r, Distributive n, Num a) => m (r a) -> r (n a) -> m (n a) -f !*! g = fmap (\r -> Foldable.sum . liftF2 (*) r <$> g') f - where g' = distribute g +(!*!) :: (Functor m, Foldable t, Additive t, Additive n, Num a) => m (t a) -> t (n a) -> m (n a) +f !*! g = fmap (\ f' -> Foldable.foldl' (^+^) zero $ liftI2 (*^) f' g) f +infixl 6 !+! +-- | Entry-wise matrix addition. +-- +-- >>> V2 (V3 1 2 3) (V3 4 5 6) !+! V2 (V3 7 8 9) (V3 1 2 3) +-- V2 (V3 8 10 12) (V3 5 7 9) +(!+!) :: (Additive m, Additive n, Num a) => m (n a) -> m (n a) -> m (n a) +as !+! bs = liftU2 (^+^) as bs + +infixl 6 !-! +-- | Entry-wise matrix subtraction. +-- +-- >>> V2 (V3 1 2 3) (V3 4 5 6) !-! V2 (V3 7 8 9) (V3 1 2 3) +-- V2 (V3 (-6) (-6) (-6)) (V3 3 3 3) +(!-!) :: (Additive m, Additive n, Num a) => m (n a) -> m (n a) -> m (n a) +as !-! bs = liftU2 (^-^) as bs + +infixl 7 !* -- | Matrix * column vector -- -- >>> V2 (V3 1 2 3) (V3 4 5 6) !* V3 7 8 9 -- V2 50 122 -infixl 7 *! -(!*) :: (Functor m, Metric r, Num a) => m (r a) -> r a -> m a -m !* v = dot v <$> m - -infixl 7 !* +(!*) :: (Functor m, Foldable r, Additive r, Num a) => m (r a) -> r a -> m a +m !* v = fmap (\r -> Foldable.sum $ liftI2 (*) r v) m +infixl 7 *! -- | Row vector * matrix -- -- >>> V2 1 2 *! V2 (V3 3 4 5) (V3 6 7 8) -- V3 15 18 21 -(*!) :: (Metric r, Distributive n, Num a) => r a -> r (n a) -> n a -f *! g = dot f <$> distribute g +-- (*!) :: (Metric r, Additive n, Num a) => r a -> r (n a) -> n a +-- f *! g = dot f <$> distribute g + +(*!) :: (Num a, Foldable t, Additive f, Additive t) => t a -> t (f a) -> f a +f *! g = sumV $ liftI2 (*^) f g + infixl 7 *!! -- | Scalar-matrix product -- @@ -88,6 +156,12 @@ (!!*) = flip (*!!) {-# INLINE (!!*) #-} +infixl 7 !!/ +-- | Matrix-scalar division +(!!/) :: (Functor m, Functor r, Fractional a) => m (r a) -> a -> m (r a) +m !!/ s = fmap (^/ s) m +{-# INLINE (!!/) #-} + -- | Hermitian conjugate or conjugate transpose -- -- >>> adjoint (V2 (V2 (1 :+ 2) (3 :+ 4)) (V2 (5 :+ 6) (7 :+ 8))) @@ -96,46 +170,59 @@ adjoint = collect (fmap conjugate) {-# INLINE adjoint #-} --- | Compute the trace of a matrix --- --- >>> trace (V2 (V2 a b) (V2 c d)) --- a + d -trace :: (Monad f, Foldable f, Num a) => f (f a) -> a -trace m = Foldable.sum (join m) -{-# INLINE trace #-} - -- * Matrices -- -- Matrices use a row-major representation. -- | A 2x2 matrix with row-major representation type M22 a = V2 (V2 a) +-- | A 2x3 matrix with row-major representation +type M23 a = V2 (V3 a) +-- | A 2x4 matrix with row-major representation +type M24 a = V2 (V4 a) +-- | A 3x2 matrix with row-major representation +type M32 a = V3 (V2 a) -- | A 3x3 matrix with row-major representation type M33 a = V3 (V3 a) --- | A 4x4 matrix with row-major representation -type M44 a = V4 (V4 a) +-- | A 3x4 matrix with row-major representation +type M34 a = V3 (V4 a) +-- | A 4x2 matrix with row-major representation +type M42 a = V4 (V2 a) -- | A 4x3 matrix with row-major representation type M43 a = V4 (V3 a) +-- | A 4x4 matrix with row-major representation +type M44 a = V4 (V4 a) -- | Build a rotation matrix from a unit 'Quaternion'. fromQuaternion :: Num a => Quaternion a -> M33 a fromQuaternion (Quaternion w (V3 x y z)) = - V3 (V3 (1-2*(y2+z2)) (2*(x*y-z*w)) (2*(x*z+y*w))) - (V3 (2*(x*y+z*w)) (1-2*(x2+z2)) (2*(y*z-x*w))) - (V3 (2*(x*z-y*w)) (2*(y*z+x*w)) (1-2*(x2+y2))) - where x2 = x * x - y2 = y * y - z2 = z * z + V3 (V3 (1-2*(y2+z2)) (2*(xy-zw)) (2*(xz+yw))) + (V3 (2*(xy+zw)) (1-2*(x2+z2)) (2*(yz-xw))) + (V3 (2*(xz-yw)) (2*(yz+xw)) (1-2*(x2+y2))) + where x2 = x*x + y2 = y*y + z2 = z*z + xy = x*y + xz = x*z + xw = x*w + yz = y*z + yw = y*w + zw = z*w +{-# INLINE fromQuaternion #-} +-- | Build a transformation matrix from a rotation matrix and a +-- translation vector. mkTransformationMat :: Num a => M33 a -> V3 a -> M44 a mkTransformationMat (V3 r1 r2 r3) (V3 tx ty tz) = V4 (snoc3 r1 tx) (snoc3 r2 ty) (snoc3 r3 tz) (V4 0 0 0 1) where snoc3 (V3 x y z) = V4 x y z +{-# INLINE mkTransformationMat #-} -- |Build a transformation matrix from a rotation expressed as a -- 'Quaternion' and a translation vector. mkTransformation :: Num a => Quaternion a -> V3 a -> M44 a mkTransformation = mkTransformationMat . fromQuaternion +{-# INLINE mkTransformation #-} -- | Convert from a 4x3 matrix to a 4x4 matrix, extending it with the @[ 0 0 0 1 ]@ column vector m43_to_m44 :: Num a => M43 a -> M44 a @@ -148,39 +235,78 @@ (V4 d e f 0) (V4 g h i 0) (V4 j k l 1) -{-# ANN m43_to_m44 "HLint: ignore Use camelCase" #-} -- | Convert a 3x3 matrix to a 4x4 matrix extending it with 0's in the new row and column. m33_to_m44 :: Num a => M33 a -> M44 a m33_to_m44 (V3 r1 r2 r3) = V4 (vector r1) (vector r2) (vector r3) (point 0) -{-# ANN m33_to_m44 "HLint: ignore Use camelCase" #-} --- |3x3 identity matrix. +-- |The identity matrix for any dimension vector. -- --- >>> eye3 +-- >>> identity :: M44 Int +-- V4 (V4 1 0 0 0) (V4 0 1 0 0) (V4 0 0 1 0) (V4 0 0 0 1) +-- >>> identity :: V3 (V3 Int) -- V3 (V3 1 0 0) (V3 0 1 0) (V3 0 0 1) -eye3 :: Num a => M33 a -eye3 = V3 (V3 1 0 0) - (V3 0 1 0) - (V3 0 0 1) +identity :: (Num a, Traversable t, Applicative t) => t (t a) +identity = scaled (pure 1) --- |4x4 identity matrix. --- --- >>> eye4 --- V4 (V4 1 0 0 0) (V4 0 1 0 0) (V4 0 0 1 0) (V4 0 0 0 1) -eye4 :: Num a => M44 a -eye4 = V4 (V4 1 0 0 0) - (V4 0 1 0 0) - (V4 0 0 1 0) - (V4 0 0 0 1) +-- |Extract the translation vector (first three entries of the last +-- column) from a 3x4 or 4x4 matrix. +translation :: (Representable t, R3 t, R4 v) => Lens' (t (v a)) (V3 a) +translation = column _w._xyz +{- +translation f rs = aux <$> f (view _w <$> view _xyz rs) + where aux (V3 x y z) = (_x._w .~ x) . (_y._w .~ y) . (_z._w .~ z) $ rs +-- translation :: (R3 t, R4 v, Functor f, Functor t) => (V3 a -> f (V3 a)) -> t (v a) -> f (t a) +-- translation = (. fmap (^._w)) . _xyz where +-- x ^. l = getConst (l Const x) +-} --- |Extract the translation vector (first three entries of the last --- column) from a 3x4 or 4x4 matrix -translation :: (R3 t, R4 v, Functor f, Functor t) => (V3 a -> f (V3 a)) -> t (v a) -> f (t a) -translation = (. fmap (^._w)) . _xyz where - x ^. l = getConst (l Const x) +-- |Extract a 2x2 matrix from a matrix of higher dimensions by dropping excess +-- rows and columns. +_m22 :: (Representable t, R2 t, R2 v) => Lens' (t (v a)) (M22 a) +_m22 = column _xy._xy +-- |Extract a 2x3 matrix from a matrix of higher dimensions by dropping excess +-- rows and columns. +_m23 :: (Representable t, R2 t, R3 v) => Lens' (t (v a)) (M23 a) +_m23 = column _xyz._xy + +-- |Extract a 2x4 matrix from a matrix of higher dimensions by dropping excess +-- rows and columns. +_m24 :: (Representable t, R2 t, R4 v) => Lens' (t (v a)) (M24 a) +_m24 = column _xyzw._xy + +-- |Extract a 3x2 matrix from a matrix of higher dimensions by dropping excess +-- rows and columns. +_m32 :: (Representable t, R3 t, R2 v) => Lens' (t (v a)) (M32 a) +_m32 = column _xy._xyz + +-- |Extract a 3x3 matrix from a matrix of higher dimensions by dropping excess +-- rows and columns. +_m33 :: (Representable t, R3 t, R3 v) => Lens' (t (v a)) (M33 a) +_m33 = column _xyz._xyz + +-- |Extract a 3x4 matrix from a matrix of higher dimensions by dropping excess +-- rows and columns. +_m34 :: (Representable t, R3 t, R4 v) => Lens' (t (v a)) (M34 a) +_m34 = column _xyzw._xyz + +-- |Extract a 4x2 matrix from a matrix of higher dimensions by dropping excess +-- rows and columns. +_m42 :: (Representable t, R4 t, R2 v) => Lens' (t (v a)) (M42 a) +_m42 = column _xy._xyzw + +-- |Extract a 4x3 matrix from a matrix of higher dimensions by dropping excess +-- rows and columns. +_m43 :: (Representable t, R4 t, R3 v) => Lens' (t (v a)) (M43 a) +_m43 = column _xyz._xyzw + +-- |Extract a 4x4 matrix from a matrix of higher dimensions by dropping excess +-- rows and columns. +_m44 :: (Representable t, R4 t, R4 v) => Lens' (t (v a)) (M44 a) +_m44 = column _xyzw._xyzw + -- |2x2 matrix determinant. -- -- >>> det22 (V2 (V2 a b) (V2 c d)) @@ -199,29 +325,49 @@ (V3 g h i)) = a * (e*i-f*h) - d * (b*i-c*h) + g * (b*f-c*e) {-# INLINE det33 #-} +-- |4x4 matrix determinant. +det44 :: Num a => M44 a -> a +det44 (V4 (V4 i00 i01 i02 i03) + (V4 i10 i11 i12 i13) + (V4 i20 i21 i22 i23) + (V4 i30 i31 i32 i33)) = + let + s0 = i00 * i11 - i10 * i01 + s1 = i00 * i12 - i10 * i02 + s2 = i00 * i13 - i10 * i03 + s3 = i01 * i12 - i11 * i02 + s4 = i01 * i13 - i11 * i03 + s5 = i02 * i13 - i12 * i03 + + c5 = i22 * i33 - i32 * i23 + c4 = i21 * i33 - i31 * i23 + c3 = i21 * i32 - i31 * i22 + c2 = i20 * i33 - i30 * i23 + c1 = i20 * i32 - i30 * i22 + c0 = i20 * i31 - i30 * i21 + in s0 * c5 - s1 * c4 + s2 * c3 + s3 * c2 - s4 * c1 + s5 * c0 +{-# INLINE det44 #-} + -- |2x2 matrix inverse. -- -- >>> inv22 $ V2 (V2 1 2) (V2 3 4) --- Just (V2 (V2 (-2.0) 1.0) (V2 1.5 (-0.5))) -inv22 :: (Epsilon a, Floating a) => M22 a -> Maybe (M22 a) -inv22 m@(V2 (V2 a b) (V2 c d)) - | nearZero det = Nothing - | otherwise = Just $ (1 / det) *!! V2 (V2 d (-b)) (V2 (-c) a) +-- V2 (V2 (-2.0) 1.0) (V2 1.5 (-0.5)) +inv22 :: Fractional a => M22 a -> M22 a +inv22 m@(V2 (V2 a b) (V2 c d)) = (1 / det) *!! V2 (V2 d (-b)) (V2 (-c) a) where det = det22 m {-# INLINE inv22 #-} -- |3x3 matrix inverse. -- -- >>> inv33 $ V3 (V3 1 2 4) (V3 4 2 2) (V3 1 1 1) --- Just (V3 (V3 0.0 0.5 (-1.0)) (V3 (-0.5) (-0.75) 3.5) (V3 0.5 0.25 (-1.5))) -inv33 :: (Epsilon a, Floating a) => M33 a -> Maybe (M33 a) +-- V3 (V3 0.0 0.5 (-1.0)) (V3 (-0.5) (-0.75) 3.5) (V3 0.5 0.25 (-1.5)) +inv33 :: Fractional a => M33 a -> M33 a inv33 m@(V3 (V3 a b c) (V3 d e f) (V3 g h i)) - | nearZero det = Nothing - | otherwise = Just $ (1 / det) *!! V3 (V3 a' b' c') - (V3 d' e' f') - (V3 g' h' i') + = (1 / det) *!! V3 (V3 a' b' c') + (V3 d' e' f') + (V3 g' h' i') where a' = cofactor (e,f,h,i) b' = cofactor (c,b,i,h) c' = cofactor (b,c,e,f) @@ -234,3 +380,352 @@ cofactor (q,r,s,t) = det22 (V2 (V2 q r) (V2 s t)) det = det33 m {-# INLINE inv33 #-} + + +-- | 'transpose' is just an alias for 'distribute' +-- +-- > transpose (V3 (V2 1 2) (V2 3 4) (V2 5 6)) +-- V2 (V3 1 3 5) (V3 2 4 6) +transpose :: (Distributive g, Functor f) => f (g a) -> g (f a) +transpose = distribute +{-# INLINE transpose #-} + +-- |4x4 matrix inverse. +inv44 :: Fractional a => M44 a -> M44 a +inv44 (V4 (V4 i00 i01 i02 i03) + (V4 i10 i11 i12 i13) + (V4 i20 i21 i22 i23) + (V4 i30 i31 i32 i33)) = + let s0 = i00 * i11 - i10 * i01 + s1 = i00 * i12 - i10 * i02 + s2 = i00 * i13 - i10 * i03 + s3 = i01 * i12 - i11 * i02 + s4 = i01 * i13 - i11 * i03 + s5 = i02 * i13 - i12 * i03 + c5 = i22 * i33 - i32 * i23 + c4 = i21 * i33 - i31 * i23 + c3 = i21 * i32 - i31 * i22 + c2 = i20 * i33 - i30 * i23 + c1 = i20 * i32 - i30 * i22 + c0 = i20 * i31 - i30 * i21 + det = s0 * c5 - s1 * c4 + s2 * c3 + s3 * c2 - s4 * c1 + s5 * c0 + invDet = recip det + in invDet *!! V4 (V4 (i11 * c5 - i12 * c4 + i13 * c3) + (-i01 * c5 + i02 * c4 - i03 * c3) + (i31 * s5 - i32 * s4 + i33 * s3) + (-i21 * s5 + i22 * s4 - i23 * s3)) + (V4 (-i10 * c5 + i12 * c2 - i13 * c1) + (i00 * c5 - i02 * c2 + i03 * c1) + (-i30 * s5 + i32 * s2 - i33 * s1) + (i20 * s5 - i22 * s2 + i23 * s1)) + (V4 (i10 * c4 - i11 * c2 + i13 * c0) + (-i00 * c4 + i01 * c2 - i03 * c0) + (i30 * s4 - i31 * s2 + i33 * s0) + (-i20 * s4 + i21 * s2 - i23 * s0)) + (V4 (-i10 * c3 + i11 * c1 - i12 * c0) + (i00 * c3 - i01 * c1 + i02 * c0) + (-i30 * s3 + i31 * s1 - i32 * s0) + (i20 * s3 - i21 * s1 + i22 * s0)) +{-# INLINE inv44 #-} + +-- | Compute the (L, U) decomposition of a square matrix using Crout's +-- algorithm. The 'Index' of the vectors must be 'Integral'. +lu :: ( Num a + , Fractional a + , Foldable m + , Traversable m + , Applicative m + , Additive m + , Ixed (m a) + , Ixed (m (m a)) + , i ~ Index (m a) + , i ~ Index (m (m a)) + , Eq i + , Integral i + , a ~ IxValue (m a) + , m a ~ IxValue (m (m a)) + , Num (m a) + ) + => m (m a) + -> (m (m a), m (m a)) +lu a = + let n = fromIntegral (length a) + initU = identity + initL = zero + buildLVal !i !j !l !u = + let go !k !s + | k == j = s + | otherwise = go (k+1) + ( s + + ( (l ^?! ix i ^?! ix k) + * (u ^?! ix k ^?! ix j) + ) + ) + s' = go 0 0 + in l & (ix i . ix j) .~ ((a ^?! ix i ^?! ix j) - s') + buildL !i !j !l !u + | i == n = l + | otherwise = buildL (i+1) j (buildLVal i j l u) u + buildUVal !i !j !l !u = + let go !k !s + | k == j = s + | otherwise = go (k+1) + ( s + + ( (l ^?! ix j ^?! ix k) + * (u ^?! ix k ^?! ix i) + ) + ) + s' = go 0 0 + in u & (ix j . ix i) .~ ( ((a ^?! ix j ^?! ix i) - s') + / (l ^?! ix j ^?! ix j) + ) + buildU !i !j !l !u + | i == n = u + | otherwise = buildU (i+1) j l (buildUVal i j l u) + buildLU !j !l !u + | j == n = (l, u) + | otherwise = + let l' = buildL j j l u + u' = buildU j j l' u + in buildLU (j+1) l' u' + in buildLU 0 initL initU + +-- | Compute the (L, U) decomposition of a square matrix using Crout's +-- algorithm, using the vector's 'Finite' instance to provide an index. +luFinite :: ( Num a + , Fractional a + , Functor m + , Finite m + , n ~ Size m + , KnownNat n + , Num (m a) + ) + => m (m a) + -> (m (m a), m (m a)) +luFinite a = + bimap (fmap fromV . fromV) + (fmap fromV . fromV) + (lu (fmap toV (toV a))) + +-- | Solve a linear system with a lower-triangular matrix of coefficients with +-- forwards substitution. +forwardSub :: ( Num a + , Fractional a + , Foldable m + , Additive m + , Ixed (m a) + , Ixed (m (m a)) + , i ~ Index (m a) + , i ~ Index (m (m a)) + , Eq i + , Ord i + , Integral i + , a ~ IxValue (m a) + , m a ~ IxValue (m (m a)) + ) + => m (m a) + -> m a + -> m a +forwardSub a b = + let n = fromIntegral (length b) + initX = zero + coeff !i !j !s !x + | j == i = s + | otherwise = coeff i (j+1) (s + ((a ^?! ix i ^?! ix j) * (x ^?! ix j))) x + go !i !x + | i == n = x + | otherwise = go (i + 1) (x & ix i .~ ( ((b ^?! ix i) - coeff i 0 0 x) + / (a ^?! ix i ^?! ix i) + )) + in go 0 initX + +-- | Solve a linear system with a lower-triangular matrix of coefficients with +-- forwards substitution, using the vector's 'Finite' instance to provide an +-- index. +forwardSubFinite :: ( Num a + , Fractional a + , Foldable m + , n ~ Size m + , KnownNat n + , Additive m + , Finite m + ) + => m (m a) + -> m a + -> m a +forwardSubFinite a b = fromV (forwardSub (fmap toV (toV a)) (toV b)) + +-- | Solve a linear system with an upper-triangular matrix of coefficients with +-- backwards substitution. +backwardSub :: ( Num a + , Fractional a + , Foldable m + , Additive m + , Ixed (m a) + , Ixed (m (m a)) + , i ~ Index (m a) + , i ~ Index (m (m a)) + , Eq i + , Ord i + , Integral i + , a ~ IxValue (m a) + , m a ~ IxValue (m (m a)) + ) + => m (m a) + -> m a + -> m a +backwardSub a b = + let n = fromIntegral (length b) + initX = zero + coeff !i !j !s !x + | j == n = s + | otherwise = coeff i + (j+1) + (s + ((a ^?! ix i ^?! ix j) * (x ^?! ix j))) + x + go !i !x + | i < 0 = x + | otherwise = go (i-1) + (x & ix i .~ ( ((b ^?! ix i) - coeff i (i+1) 0 x) + / (a ^?! ix i ^?! ix i) + )) + in go (n-1) initX + +-- | Solve a linear system with an upper-triangular matrix of coefficients with +-- backwards substitution, using the vector's 'Finite' instance to provide an +-- index. +backwardSubFinite :: ( Num a + , Fractional a + , Foldable m + , n ~ Size m + , KnownNat n + , Additive m + , Finite m + ) + => m (m a) + -> m a + -> m a +backwardSubFinite a b = fromV (backwardSub (fmap toV (toV a)) (toV b)) + +-- | Solve a linear system with LU decomposition. +luSolve :: ( Num a + , Fractional a + , Foldable m + , Traversable m + , Applicative m + , Additive m + , Ixed (m a) + , Ixed (m (m a)) + , i ~ Index (m a) + , i ~ Index (m (m a)) + , Eq i + , Integral i + , a ~ IxValue (m a) + , m a ~ IxValue (m (m a)) + , Num (m a) + ) + => m (m a) + -> m a + -> m a +luSolve a b = + let (l, u) = lu a + in backwardSub u (forwardSub l b) + +-- | Solve a linear system with LU decomposition, using the vector's 'Finite' +-- instance to provide an index. +luSolveFinite :: ( Num a + , Fractional a + , Functor m + , Finite m + , n ~ Size m + , KnownNat n + , Num (m a) + ) + => m (m a) + -> m a + -> m a +luSolveFinite a b = fromV (luSolve (fmap toV (toV a)) (toV b)) + +-- | Invert a matrix with LU decomposition. +luInv :: ( Num a + , Fractional a + , Foldable m + , Traversable m + , Applicative m + , Additive m + , Distributive m + , Ixed (m a) + , Ixed (m (m a)) + , i ~ Index (m a) + , i ~ Index (m (m a)) + , Eq i + , Integral i + , a ~ IxValue (m a) + , m a ~ IxValue (m (m a)) + , Num (m a) + ) + => m (m a) + -> m (m a) +luInv a = + let n = fromIntegral (length a) + initA' = zero + (l, u) = lu a + go !i !a' + | i == n = a' + | otherwise = let e = zero & ix i .~ 1 + a'r = backwardSub u (forwardSub l e) + in go (i+1) (a' & ix i .~ a'r) + in transpose (go 0 initA') + +-- | Invert a matrix with LU decomposition, using the vector's 'Finite' instance +-- to provide an index. +luInvFinite :: ( Num a + , Fractional a + , Functor m + , Finite m + , n ~ Size m + , KnownNat n + , Num (m a) + ) + => m (m a) + -> m (m a) +luInvFinite a = fmap fromV (fromV (luInv (fmap toV (toV a)))) + +-- | Compute the determinant of a matrix using LU decomposition. +luDet :: ( Num a + , Fractional a + , Foldable m + , Traversable m + , Applicative m + , Additive m + , Trace m + , Ixed (m a) + , Ixed (m (m a)) + , i ~ Index (m a) + , i ~ Index (m (m a)) + , Eq i + , Integral i + , a ~ IxValue (m a) + , m a ~ IxValue (m (m a)) + , Num (m a) + ) + => m (m a) + -> a +luDet a = + let (l, u) = lu a + p = Foldable.foldl (*) 1 + in p (diagonal l) * p (diagonal u) + +-- | Compute the determinant of a matrix using LU decomposition, using the +-- vector's 'Finite' instance to provide an index. +luDetFinite :: ( Num a + , Fractional a + , Functor m + , Finite m + , n ~ Size m + , KnownNat n + , Num (m a) + ) + => m (m a) + -> a +luDetFinite = luDet . fmap toV . toV diff --git a/src/Linear/Metric.hs b/src/Linear/Metric.hs --- a/src/Linear/Metric.hs +++ b/src/Linear/Metric.hs @@ -1,8 +1,9 @@ +{-# LANGUAGE CPP #-} {-# LANGUAGE DefaultSignatures #-} +{-# LANGUAGE Trustworthy #-} ----------------------------------------------------------------------------- -- | --- Module : Linear.Metric --- Copyright : (C) 2012-2013 Edward Kmett, +-- Copyright : (C) 2012-2015 Edward Kmett -- License : BSD-style (see the file LICENSE) -- -- Maintainer : Edward Kmett @@ -12,16 +13,25 @@ -- Free metric spaces ---------------------------------------------------------------------------- module Linear.Metric - ( Metric(..), normalize + ( Metric(..), normalize, project ) where +import Control.Applicative import Data.Foldable as Foldable -import Data.Functor.Apply +import Data.Functor.Compose +import Data.Functor.Identity +import Data.Functor.Product +import Data.Vector (Vector) +import Data.IntMap (IntMap) +import Data.Map (Map) +import Data.HashMap.Strict (HashMap) +import Data.Hashable (Hashable) import Linear.Epsilon import Linear.Vector -- $setup -- >>> import Linear +-- -- | Free and sparse inner product/metric spaces. class Additive f => Metric f where @@ -31,8 +41,10 @@ -- >>> V2 1 2 `dot` V2 3 4 -- 11 dot :: Num a => f a -> f a -> a +#ifndef HLINT default dot :: (Foldable f, Num a) => f a -> f a -> a - dot x y = Foldable.sum $ liftF2 (*) x y + dot x y = Foldable.sum $ liftI2 (*) x y +#endif -- | Compute the squared norm. The name quadrance arises from -- Norman J. Wildberger's rational trigonometry. @@ -56,8 +68,43 @@ signorm v = fmap (/m) v where m = norm v +instance (Metric f, Metric g) => Metric (Product f g) where + dot (Pair a b) (Pair c d) = dot a c + dot b d + quadrance (Pair a b) = quadrance a + quadrance b + qd (Pair a b) (Pair c d) = qd a c + qd b d + distance p q = sqrt (qd p q) + +instance (Metric f, Metric g) => Metric (Compose f g) where + dot (Compose a) (Compose b) = quadrance (liftI2 dot a b) + quadrance = quadrance . fmap quadrance . getCompose + qd (Compose a) (Compose b) = quadrance (liftI2 qd a b) + distance (Compose a) (Compose b) = norm (liftI2 qd a b) + +instance Metric Identity where + dot (Identity x) (Identity y) = x * y + +instance Metric [] + +instance Metric Maybe + +instance Metric ZipList where + -- ZipList is missing its Foldable instance + dot (ZipList x) (ZipList y) = dot x y + +instance Metric IntMap + +instance Ord k => Metric (Map k) + +instance (Hashable k, Eq k) => Metric (HashMap k) + +instance Metric Vector + -- | Normalize a 'Metric' functor to have unit 'norm'. This function -- does not change the functor if its 'norm' is 0 or 1. normalize :: (Floating a, Metric f, Epsilon a) => f a -> f a normalize v = if nearZero l || nearZero (1-l) then v else fmap (/sqrt l) v where l = quadrance v + +-- | @project u v@ computes the projection of @v@ onto @u@. +project :: (Metric v, Fractional a) => v a -> v a -> v a +project u v = ((v `dot` u) / quadrance u) *^ u diff --git a/src/Linear/Plucker.hs b/src/Linear/Plucker.hs --- a/src/Linear/Plucker.hs +++ b/src/Linear/Plucker.hs @@ -1,8 +1,17 @@ +{-# LANGUAGE CPP #-} {-# LANGUAGE ScopedTypeVariables #-} +{-# LANGUAGE TypeFamilies #-} +{-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE MultiParamTypeClasses #-} +{-# LANGUAGE GADTs #-} +{-# LANGUAGE Trustworthy #-} +{-# LANGUAGE DeriveGeneric #-} +{-# LANGUAGE DataKinds #-} +{-# LANGUAGE DeriveLift #-} + ----------------------------------------------------------------------------- -- | --- Module : Linear.Plucker --- Copyright : (C) 2012-2013 Edward Kmett, +-- Copyright : (C) 2012-2015 Edward Kmett -- License : BSD-style (see the file LICENSE) -- -- Maintainer : Edward Kmett @@ -17,36 +26,109 @@ , isotropic , (><) , plucker + , plucker3D + -- * Operations on lines + , parallel , intersects + , LinePass(..) + , passes + , quadranceToOrigin + , closestToOrigin + , isLine + , coincides + , coincides' -- * Basis elements , p01, p02, p03 , p10, p12, p13 , p20, p21, p23 , p30, p31, p32 + + , e01, e02, e03, e12, e31, e23 ) where +#if !MIN_VERSION_base(4,18,0) import Control.Applicative +#endif +import Control.DeepSeq (NFData(rnf)) +import Control.Monad (liftM) +import Control.Monad.Fix +import Control.Monad.Zip +import Control.Lens as Lens hiding (index, (<.>)) +import Data.Binary as Binary +import Data.Bytes.Serial import Data.Distributive import Data.Foldable as Foldable +import qualified Data.Foldable.WithIndex as WithIndex import Data.Functor.Bind +import Data.Functor.Classes +import Data.Functor.Rep +import qualified Data.Functor.WithIndex as WithIndex +import Data.Hashable import Data.Semigroup import Data.Semigroup.Foldable -import Data.Semigroup.Traversable -import Data.Traversable +import Data.Serialize as Cereal +import qualified Data.Traversable.WithIndex as WithIndex +import qualified Data.Vector as V +import qualified Data.Vector.Generic.Mutable as M +import qualified Data.Vector.Generic as G +import qualified Data.Vector.Unboxed.Base as U import Foreign.Ptr (castPtr) import Foreign.Storable (Storable(..)) import GHC.Arr (Ix(..)) -import Linear.Core +import GHC.Generics (Generic, Generic1) +#if defined(MIN_VERSION_template_haskell) +import Language.Haskell.TH.Syntax (Lift) +#endif import Linear.Epsilon import Linear.Metric +import Linear.V +import Linear.V2 +import Linear.V3 import Linear.V4 import Linear.Vector - -{-# ANN module "HLint: ignore Reduce duplication" #-} +import System.Random (Random(..), Uniform) +import System.Random.Stateful (UniformRange(..)) -- | Plücker coordinates for lines in a 3-dimensional space. -data Plucker a = Plucker a a a a a a deriving (Eq,Ord,Show,Read) +data Plucker a = Plucker !a !a !a !a !a !a deriving (Eq,Ord,Show,Read + ,Generic,Generic1 +#if defined(MIN_VERSION_template_haskell) + ,Lift +#endif + ) +instance Finite Plucker where + type Size Plucker = 6 + toV (Plucker a b c d e f) = V (V.fromListN 6 [a,b,c,d,e,f]) + fromV (V v) = Plucker (v V.! 0) (v V.! 1) (v V.! 2) (v V.! 3) (v V.! 4) (v V.! 5) + +instance Random a => Random (Plucker a) where + random g = case random g of + (a, g1) -> case random g1 of + (b, g2) -> case random g2 of + (c, g3) -> case random g3 of + (d, g4) -> case random g4 of + (e, g5) -> case random g5 of + (f, g6) -> (Plucker a b c d e f, g6) + randomR (Plucker a b c d e f, Plucker a' b' c' d' e' f') g = case randomR (a,a') g of + (a'', g1) -> case randomR (b,b') g1 of + (b'', g2) -> case randomR (c,c') g2 of + (c'', g3) -> case randomR (d,d') g3 of + (d'', g4) -> case randomR (e,e') g4 of + (e'', g5) -> case randomR (f,f') g5 of + (f'', g6) -> (Plucker a'' b'' c'' d'' e'' f'', g6) + +instance Uniform a => Uniform (Plucker a) where + +instance UniformRange a => UniformRange (Plucker a) where + uniformRM (Plucker a b c d e f, Plucker a' b' c' d' e' f') g = Plucker + <$> uniformRM (a, a') g + <*> uniformRM (b, b') g + <*> uniformRM (c, c') g + <*> uniformRM (d, d') g + <*> uniformRM (e, e') g + <*> uniformRM (f, f') g + instance Functor Plucker where fmap g (Plucker a b c d e f) = Plucker (g a) (g b) (g c) (g d) (g e) (g f) {-# INLINE fmap #-} @@ -63,7 +145,13 @@ Plucker (a g) (b h) (c i) (d j) (e k) (f l) {-# INLINE (<*>) #-} -instance Additive Plucker +instance Additive Plucker where + zero = pure 0 + {-# INLINE zero #-} + liftU2 = liftA2 + {-# INLINE liftU2 #-} + liftI2 = liftA2 + {-# INLINE liftI2 #-} instance Bind Plucker where Plucker a b c d e f >>- g = Plucker a' b' c' d' e' f' where @@ -76,8 +164,10 @@ {-# INLINE (>>-) #-} instance Monad Plucker where +#if !(MIN_VERSION_base(4,11,0)) return a = Plucker a a a a a a {-# INLINE return #-} +#endif Plucker a b c d e f >>= g = Plucker a' b' c' d' e' f' where Plucker a' _ _ _ _ _ = g a Plucker _ b' _ _ _ _ = g b @@ -96,14 +186,19 @@ (fmap (\(Plucker _ _ _ _ _ x) -> x) f) {-# INLINE distribute #-} -instance Core Plucker where - core f = Plucker (f p01) (f p02) (f p03) (f p23) (f p31) (f p12) - {-# INLINE core #-} +instance Representable Plucker where + type Rep Plucker = E Plucker + tabulate f = Plucker (f e01) (f e02) (f e03) (f e23) (f e31) (f e12) + {-# INLINE tabulate #-} + index xs (E l) = view l xs + {-# INLINE index #-} instance Foldable Plucker where foldMap g (Plucker a b c d e f) = g a `mappend` g b `mappend` g c `mappend` g d `mappend` g e `mappend` g f {-# INLINE foldMap #-} + null _ = False + length _ = 6 instance Traversable Plucker where traverse g (Plucker a b c d e f) = @@ -170,6 +265,48 @@ fromRational = pure . fromRational {-# INLINE fromRational #-} +instance Floating a => Floating (Plucker a) where + pi = pure pi + {-# INLINE pi #-} + exp = fmap exp + {-# INLINE exp #-} + sqrt = fmap sqrt + {-# INLINE sqrt #-} + log = fmap log + {-# INLINE log #-} + (**) = liftA2 (**) + {-# INLINE (**) #-} + logBase = liftA2 logBase + {-# INLINE logBase #-} + sin = fmap sin + {-# INLINE sin #-} + tan = fmap tan + {-# INLINE tan #-} + cos = fmap cos + {-# INLINE cos #-} + asin = fmap asin + {-# INLINE asin #-} + atan = fmap atan + {-# INLINE atan #-} + acos = fmap acos + {-# INLINE acos #-} + sinh = fmap sinh + {-# INLINE sinh #-} + tanh = fmap tanh + {-# INLINE tanh #-} + cosh = fmap cosh + {-# INLINE cosh #-} + asinh = fmap asinh + {-# INLINE asinh #-} + atanh = fmap atanh + {-# INLINE atanh #-} + acosh = fmap acosh + {-# INLINE acosh #-} + +instance Hashable a => Hashable (Plucker a) where + hashWithSalt s (Plucker a b c d e f) = s `hashWithSalt` a `hashWithSalt` b `hashWithSalt` c `hashWithSalt` d `hashWithSalt` e `hashWithSalt` f + {-# INLINE hashWithSalt #-} + instance Storable a => Storable (Plucker a) where sizeOf _ = 6 * sizeOf (undefined::a) {-# INLINE sizeOf #-} @@ -193,30 +330,46 @@ where ptr' = castPtr ptr {-# INLINE peek #-} --- | Given a pair of points represented by homogeneous coordinates generate Plücker coordinates --- for the line through them. +instance Metric Plucker where + dot (Plucker a b c d e f) (Plucker g h i j k l) = a*g+b*h+c*i+d*j+e*k+f*l + {-# INLINE dot #-} + +instance Epsilon a => Epsilon (Plucker a) where + nearZero = nearZero . quadrance + {-# INLINE nearZero #-} + +-- | Given a pair of points represented by homogeneous coordinates +-- generate Plücker coordinates for the line through them, directed +-- from the second towards the first. plucker :: Num a => V4 a -> V4 a -> Plucker a plucker (V4 a b c d) (V4 e f g h) = Plucker (a*f-b*e) (a*g-c*e) - (a*d-h*e) - (c*h-d*g) - (d*f-b*h) (b*g-c*f) + (a*h-d*e) + (b*h-d*f) + (c*h-d*g) {-# INLINE plucker #-} +-- | Given a pair of 3D points, generate Plücker coordinates for the +-- line through them, directed from the second towards the first. +plucker3D :: Num a => V3 a -> V3 a -> Plucker a +plucker3D p q = Plucker a b c d e f + where V3 a b c = p - q + V3 d e f = p `cross` q + -- | These elements form a basis for the Plücker space, or the Grassmanian manifold @Gr(2,V4)@. -- -- @ --- 'p01' :: Lens' ('Plucker' a) a --- 'p02' :: Lens' ('Plucker' a) a --- 'p03' :: Lens' ('Plucker' a) a --- 'p23' :: Lens' ('Plucker' a) a --- 'p31' :: Lens' ('Plucker' a) a --- 'p12' :: Lens' ('Plucker' a) a +-- 'p01' :: 'Lens'' ('Plucker' a) a +-- 'p02' :: 'Lens'' ('Plucker' a) a +-- 'p03' :: 'Lens'' ('Plucker' a) a +-- 'p23' :: 'Lens'' ('Plucker' a) a +-- 'p31' :: 'Lens'' ('Plucker' a) a +-- 'p12' :: 'Lens'' ('Plucker' a) a -- @ -p01, p02, p03, p23, p31, p12 :: Functor f => (a -> f a) -> Plucker a -> f (Plucker a) +p01, p02, p03, p23, p31, p12 :: Lens' (Plucker a) a p01 g (Plucker a b c d e f) = (\a' -> Plucker a' b c d e f) <$> g a p02 g (Plucker a b c d e f) = (\b' -> Plucker a b' c d e f) <$> g b p03 g (Plucker a b c d e f) = (\c' -> Plucker a b c' d e f) <$> g c @@ -233,12 +386,12 @@ -- | These elements form an alternate basis for the Plücker space, or the Grassmanian manifold @Gr(2,V4)@. -- -- @ --- 'p10' :: 'Num' a => Lens' ('Plucker' a) a --- 'p20' :: 'Num' a => Lens' ('Plucker' a) a --- 'p30' :: 'Num' a => Lens' ('Plucker' a) a --- 'p32' :: 'Num' a => Lens' ('Plucker' a) a --- 'p13' :: 'Num' a => Lens' ('Plucker' a) a --- 'p21' :: 'Num' a => Lens' ('Plucker' a) a +-- 'p10' :: 'Num' a => 'Lens'' ('Plucker' a) a +-- 'p20' :: 'Num' a => 'Lens'' ('Plucker' a) a +-- 'p30' :: 'Num' a => 'Lens'' ('Plucker' a) a +-- 'p32' :: 'Num' a => 'Lens'' ('Plucker' a) a +-- 'p13' :: 'Num' a => 'Lens'' ('Plucker' a) a +-- 'p21' :: 'Num' a => 'Lens'' ('Plucker' a) a -- @ p10, p20, p30, p32, p13, p21 :: (Functor f, Num a) => (a -> f a) -> Plucker a -> f (Plucker a) p10 = anti p01 @@ -257,35 +410,296 @@ anti :: (Functor f, Num a) => ((a -> f a) -> r) -> (a -> f a) -> r anti k f = k (fmap negate . f . negate) +e01, e02, e03, e23, e31, e12 :: E Plucker +e01 = E p01 +e02 = E p02 +e03 = E p03 +e23 = E p23 +e31 = E p31 +e12 = E p12 + +instance WithIndex.FunctorWithIndex (E Plucker) Plucker where + imap f (Plucker a b c d e g) = Plucker (f e01 a) (f e02 b) (f e03 c) (f e23 d) (f e31 e) (f e12 g) + {-# INLINE imap #-} + +instance WithIndex.FoldableWithIndex (E Plucker) Plucker where + ifoldMap f (Plucker a b c d e g) = f e01 a `mappend` f e02 b `mappend` f e03 c + `mappend` f e23 d `mappend` f e31 e `mappend` f e12 g + {-# INLINE ifoldMap #-} + +instance WithIndex.TraversableWithIndex (E Plucker) Plucker where + itraverse f (Plucker a b c d e g) = Plucker <$> f e01 a <*> f e02 b <*> f e03 c + <*> f e23 d <*> f e31 e <*> f e12 g + {-# INLINE itraverse #-} + +#if !MIN_VERSION_lens(5,0,0) +instance Lens.FunctorWithIndex (E Plucker) Plucker where imap = WithIndex.imap +instance Lens.FoldableWithIndex (E Plucker) Plucker where ifoldMap = WithIndex.ifoldMap +instance Lens.TraversableWithIndex (E Plucker) Plucker where itraverse = WithIndex.itraverse +#endif + +type instance Index (Plucker a) = E Plucker +type instance IxValue (Plucker a) = a + +instance Ixed (Plucker a) where + ix i = el i + {-# INLINE ix #-} + +instance Each (Plucker a) (Plucker b) a b where + each = traverse + {-# INLINE each #-} + + -- | Valid Plücker coordinates @p@ will have @'squaredError' p '==' 0@ -- -- That said, floating point makes a mockery of this claim, so you may want to use 'nearZero'. -squaredError :: (Eq a, Num a) => Plucker a -> a +squaredError :: Num a => Plucker a -> a squaredError v = v >< v {-# INLINE squaredError #-} -- | This isn't th actual metric because this bilinear form gives rise to an isotropic quadratic space infixl 5 >< (><) :: Num a => Plucker a -> Plucker a -> a -Plucker a b c d e f >< Plucker g h i j k l = a*g+b*h+c*i-d*j-e*k-f*l +Plucker a b c d e f >< Plucker g h i j k l = a*l-b*k+c*j+d*i-e*h+f*g {-# INLINE (><) #-} --- | Checks if the line is near-isotropic (isotropic vectors in this quadratic space represent lines in real 3d space) +-- | Checks if the line is near-isotropic (isotropic vectors in this +-- quadratic space represent lines in real 3d space). isotropic :: Epsilon a => Plucker a -> Bool isotropic a = nearZero (a >< a) {-# INLINE isotropic #-} --- | Checks if the two vectors intersect (or nearly intersect) -intersects :: Epsilon a => Plucker a -> Plucker a -> Bool -intersects a b = nearZero (a >< b) +-- | Checks if two lines intersect (or nearly intersect). +intersects :: (Epsilon a, Ord a) => Plucker a -> Plucker a -> Bool +intersects a b = not (a `parallel` b) && passes a b == Coplanar +-- intersects :: Epsilon a => Plucker a -> Plucker a -> Bool +-- intersects a b = nearZero (a >< b) {-# INLINE intersects #-} -instance Metric Plucker where - dot (Plucker a b c d e f) (Plucker g h i j k l) = a*g+b*h+c*i+d*j+e*k+f*l - {-# INLINE dot #-} +-- | Describe how two lines pass each other. +data LinePass = Coplanar + -- ^ The lines are coplanar (parallel or intersecting). + | Clockwise + -- ^ The lines pass each other clockwise (right-handed + -- screw) + | Counterclockwise + -- ^ The lines pass each other counterclockwise + -- (left-handed screw). + deriving (Eq, Show,Generic) -instance Epsilon a => Epsilon (Plucker a) where - nearZero = nearZero . quadrance - {-# INLINE nearZero #-} +-- | Check how two lines pass each other. @passes l1 l2@ describes +-- @l2@ when looking down @l1@. +passes :: (Epsilon a, Ord a) => Plucker a -> Plucker a -> LinePass +passes a b + | nearZero s = Coplanar + | s > 0 = Counterclockwise + | otherwise = Clockwise + where s = (u1 `dot` v2) + (u2 `dot` v1) + V2 u1 v1 = toUV a + V2 u2 v2 = toUV b +{-# INLINE passes #-} +-- | Checks if two lines are parallel. +parallel :: Epsilon a => Plucker a -> Plucker a -> Bool +parallel a b = nearZero $ u1 `cross` u2 + where V2 u1 _ = toUV a + V2 u2 _ = toUV b +{-# INLINE parallel #-} + +-- | Represent a Plücker coordinate as a pair of 3-tuples, typically +-- denoted U and V. +toUV :: Plucker a -> V2 (V3 a) +toUV (Plucker a b c d e f) = V2 (V3 a b c) (V3 d e f) + +-- | Checks if two lines coincide in space. In other words, undirected equality. +coincides :: (Epsilon a, Fractional a) => Plucker a -> Plucker a -> Bool +coincides p1 p2 = Foldable.all nearZero $ (s *^ p2) - p1 + where s = maybe 1 getFirst . getOptionCompat . fold $ saveDiv <$> p1 <*> p2 + saveDiv x y | nearZero y = optionCompat Nothing + | otherwise = optionCompat . Just $ First (x / y) +{-# INLINABLE coincides #-} + +-- | Checks if two lines coincide in space, and have the same +-- orientation. +coincides' :: (Epsilon a, Fractional a, Ord a) => Plucker a -> Plucker a -> Bool +coincides' p1 p2 = Foldable.all nearZero ((s *^ p2) - p1) && s > 0 + where s = maybe 1 getFirst . getOptionCompat . fold $ saveDiv <$> p1 <*> p2 + saveDiv x y | nearZero y = optionCompat Nothing + | otherwise = optionCompat . Just $ First (x / y) +{-# INLINABLE coincides' #-} + +-- The coincides and coincides' functions above require the use of a Maybe type +-- with the following Monoid instance: +-- +-- instance Semigroup a => Monoid (Maybe a) where ... +-- +-- Unfortunately, Maybe has only had such an instance since base-4.11. Prior +-- to that, its Monoid instance had an instance context of Monoid a, which is +-- too strong. To compensate, we use CPP to define an OptionCompat type +-- synonym, which is an alias for Maybe on recent versions of base and an alias +-- for Data.Semigroup.Option on older versions of base. We don't want to use +-- Option on recent versions of base, as it is deprecated. +#if MIN_VERSION_base(4,11,0) +type OptionCompat = Maybe + +optionCompat :: Maybe a -> OptionCompat a +optionCompat = id + +getOptionCompat :: OptionCompat a -> Maybe a +getOptionCompat = id +#else +type OptionCompat = Option + +optionCompat :: Maybe a -> OptionCompat a +optionCompat = Option + +getOptionCompat :: OptionCompat a -> Maybe a +getOptionCompat = getOption +#endif + +-- | The minimum squared distance of a line from the origin. +quadranceToOrigin :: Fractional a => Plucker a -> a +quadranceToOrigin p = (v `dot` v) / (u `dot` u) + where V2 u v = toUV p +{-# INLINE quadranceToOrigin #-} + +-- | The point where a line is closest to the origin. +closestToOrigin :: Fractional a => Plucker a -> V3 a +closestToOrigin p = normalizePoint $ V4 x y z (u `dot` u) + where V2 u v = toUV p + V3 x y z = v `cross` u +{-# INLINE closestToOrigin #-} + +-- | Not all 6-dimensional points correspond to a line in 3D. This +-- predicate tests that a Plücker coordinate lies on the Grassmann +-- manifold, and does indeed represent a 3D line. +isLine :: Epsilon a => Plucker a -> Bool +isLine p = nearZero $ u `dot` v + where V2 u v = toUV p +{-# INLINE isLine #-} + -- TODO: drag some more stuff out of my thesis + +data instance U.Vector (Plucker a) = V_Plucker !Int (U.Vector a) +data instance U.MVector s (Plucker a) = MV_Plucker !Int (U.MVector s a) +instance U.Unbox a => U.Unbox (Plucker a) + +instance U.Unbox a => M.MVector U.MVector (Plucker a) where + basicLength (MV_Plucker n _) = n + basicUnsafeSlice m n (MV_Plucker _ v) = MV_Plucker n (M.basicUnsafeSlice (6*m) (6*n) v) + basicOverlaps (MV_Plucker _ v) (MV_Plucker _ u) = M.basicOverlaps v u + basicUnsafeNew n = liftM (MV_Plucker n) (M.basicUnsafeNew (6*n)) + basicUnsafeRead (MV_Plucker _ a) i = + do let o = 6*i + x <- M.basicUnsafeRead a o + y <- M.basicUnsafeRead a (o+1) + z <- M.basicUnsafeRead a (o+2) + w <- M.basicUnsafeRead a (o+3) + v <- M.basicUnsafeRead a (o+4) + u <- M.basicUnsafeRead a (o+5) + return (Plucker x y z w v u) + basicUnsafeWrite (MV_Plucker _ a) i (Plucker x y z w v u) = + do let o = 6*i + M.basicUnsafeWrite a o x + M.basicUnsafeWrite a (o+1) y + M.basicUnsafeWrite a (o+2) z + M.basicUnsafeWrite a (o+3) w + M.basicUnsafeWrite a (o+4) v + M.basicUnsafeWrite a (o+5) u + basicInitialize (MV_Plucker _ v) = M.basicInitialize v + +instance U.Unbox a => G.Vector U.Vector (Plucker a) where + basicUnsafeFreeze (MV_Plucker n v) = liftM ( V_Plucker n) (G.basicUnsafeFreeze v) + basicUnsafeThaw ( V_Plucker n v) = liftM (MV_Plucker n) (G.basicUnsafeThaw v) + basicLength ( V_Plucker n _) = n + basicUnsafeSlice m n (V_Plucker _ v) = V_Plucker n (G.basicUnsafeSlice (6*m) (6*n) v) + basicUnsafeIndexM (V_Plucker _ a) i = + do let o = 6*i + x <- G.basicUnsafeIndexM a o + y <- G.basicUnsafeIndexM a (o+1) + z <- G.basicUnsafeIndexM a (o+2) + w <- G.basicUnsafeIndexM a (o+3) + v <- G.basicUnsafeIndexM a (o+4) + u <- G.basicUnsafeIndexM a (o+5) + return (Plucker x y z w v u) + +instance MonadZip Plucker where + mzipWith = liftA2 + +instance MonadFix Plucker where + mfix f = Plucker (let Plucker a _ _ _ _ _ = f a in a) + (let Plucker _ a _ _ _ _ = f a in a) + (let Plucker _ _ a _ _ _ = f a in a) + (let Plucker _ _ _ a _ _ = f a in a) + (let Plucker _ _ _ _ a _ = f a in a) + (let Plucker _ _ _ _ _ a = f a in a) + +instance NFData a => NFData (Plucker a) where + rnf (Plucker a b c d e f) = rnf a `seq` rnf b `seq` rnf c + `seq` rnf d `seq` rnf e `seq` rnf f + +instance Serial1 Plucker where + serializeWith = traverse_ + deserializeWith k = Plucker <$> k <*> k <*> k <*> k <*> k <*> k + +instance Serial a => Serial (Plucker a) where + serialize = serializeWith serialize + deserialize = deserializeWith deserialize + +instance Binary a => Binary (Plucker a) where + put = serializeWith Binary.put + get = deserializeWith Binary.get + +instance Serialize a => Serialize (Plucker a) where + put = serializeWith Cereal.put + get = deserializeWith Cereal.get + +instance Eq1 Plucker where + liftEq k (Plucker a1 b1 c1 d1 e1 f1) + (Plucker a2 b2 c2 d2 e2 f2) + = k a1 a2 && k b1 b2 && k c1 c2 && k d1 d2 && k e1 e2 && k f1 f2 +instance Ord1 Plucker where + liftCompare k (Plucker a1 b1 c1 d1 e1 f1) + (Plucker a2 b2 c2 d2 e2 f2) + = k a1 a2 `mappend` k b1 b2 `mappend` k c1 c2 `mappend` k d1 d2 `mappend` k e1 e2 `mappend` k f1 f2 +instance Read1 Plucker where + liftReadsPrec k _ z = readParen (z > 10) $ \r -> + [ (Plucker a b c d e f, r7) + | ("Plucker",r1) <- lex r + , (a,r2) <- k 11 r1 + , (b,r3) <- k 11 r2 + , (c,r4) <- k 11 r3 + , (d,r5) <- k 11 r4 + , (e,r6) <- k 11 r5 + , (f,r7) <- k 11 r6 + ] +instance Show1 Plucker where + liftShowsPrec k _ z (Plucker a b c d e f) = showParen (z > 10) $ + showString "Plucker " . k 11 a . showChar ' ' . k 11 b . showChar ' ' . k 11 c . showChar ' ' . k 11 d . showChar ' ' . k 11 e . showChar ' ' . k 11 f + +instance Field1 (Plucker a) (Plucker a) a a where + _1 f (Plucker x y z u v w) = f x <&> \x' -> Plucker x' y z u v w + +instance Field2 (Plucker a) (Plucker a) a a where + _2 f (Plucker x y z u v w) = f y <&> \y' -> Plucker x y' z u v w + +instance Field3 (Plucker a) (Plucker a) a a where + _3 f (Plucker x y z u v w) = f z <&> \z' -> Plucker x y z' u v w + +instance Field4 (Plucker a) (Plucker a) a a where + _4 f (Plucker x y z u v w) = f u <&> \u' -> Plucker x y z u' v w + +instance Field5 (Plucker a) (Plucker a) a a where + _5 f (Plucker x y z u v w) = f v <&> \v' -> Plucker x y z u v' w + +instance Field6 (Plucker a) (Plucker a) a a where + _6 f (Plucker x y z u v w) = f w <&> \w' -> Plucker x y z u v w' + +instance Semigroup a => Semigroup (Plucker a) where + (<>) = liftA2 (<>) + +instance Monoid a => Monoid (Plucker a) where + mempty = pure mempty +#if !(MIN_VERSION_base(4,11,0)) + mappend = liftA2 mappend +#endif diff --git a/src/Linear/Plucker/Coincides.hs b/src/Linear/Plucker/Coincides.hs new file mode 100644 --- /dev/null +++ b/src/Linear/Plucker/Coincides.hs @@ -0,0 +1,38 @@ +{-# LANGUAGE GADTs #-} +--------------------------------------------------------------------------------- +-- | +-- Copyright : (C) 2012-2015 Edward Kmett +-- License : BSD-style (see the file LICENSE) +-- +-- Maintainer : Edward Kmett +-- Stability : experimental +-- Portability : non-portable +-- +-- Utility for working with Plücker coordinates for lines in 3d homogeneous space. +---------------------------------------------------------------------------------- +module Linear.Plucker.Coincides + ( Coincides(..) + ) where + +import Linear.Epsilon +import Linear.Plucker + +-- | When lines are represented as Plücker coordinates, we have the +-- ability to check for both directed and undirected +-- equality. Undirected equality between 'Line's (or a 'Line' and a +-- 'Ray') checks that the two lines coincide in 3D space. Directed +-- equality, between two 'Ray's, checks that two lines coincide in 3D, +-- and have the same direction. To accomodate these two notions of +-- equality, we use an 'Eq' instance on the 'Coincides' data type. +-- +-- For example, to check the /directed/ equality between two lines, +-- @p1@ and @p2@, we write, @Ray p1 == Ray p2@. +data Coincides a where + Line :: (Epsilon a, Fractional a) => Plucker a -> Coincides a + Ray :: (Epsilon a, Fractional a, Ord a) => Plucker a -> Coincides a + +instance Eq (Coincides a) where + Line a == Line b = coincides a b + Line a == Ray b = coincides a b + Ray a == Line b = coincides a b + Ray a == Ray b = coincides' a b diff --git a/src/Linear/Projection.hs b/src/Linear/Projection.hs new file mode 100644 --- /dev/null +++ b/src/Linear/Projection.hs @@ -0,0 +1,260 @@ +{-# LANGUAGE CPP #-} +--------------------------------------------------------------------------- +-- | +-- Copyright : (C) 2015 Edward Kmett +-- License : BSD-style (see the file LICENSE) +-- +-- Maintainer : Edward Kmett +-- Stability : experimental +-- Portability : non-portable +-- +-- Common projection matrices: e.g. perspective/orthographic transformation +-- matrices. +-- +-- Analytically derived inverses are also supplied, because they can be +-- much more accurate in practice than computing them through general +-- purpose means +--------------------------------------------------------------------------- +module Linear.Projection + ( lookAt + , perspective, inversePerspective + , infinitePerspective, inverseInfinitePerspective + , frustum, inverseFrustum + , ortho, inverseOrtho + ) where + +import Control.Lens hiding (index) +import Linear.V3 +import Linear.V4 +import Linear.Matrix +import Linear.Epsilon +import Linear.Metric + +-- $setup +-- >>> import Linear.Matrix +-- >>> import Linear.V2 +-- >>> import Linear.V4 + +-- | Build a look at view matrix +lookAt + :: (Epsilon a, Floating a) + => V3 a -- ^ Eye + -> V3 a -- ^ Center + -> V3 a -- ^ Up + -> M44 a +lookAt eye center up = + V4 (V4 (xa^._x) (xa^._y) (xa^._z) xd) + (V4 (ya^._x) (ya^._y) (ya^._z) yd) + (V4 (-za^._x) (-za^._y) (-za^._z) zd) + (V4 0 0 0 1) + where za = normalize $ center - eye + xa = normalize $ cross za up + ya = cross xa za + xd = -dot xa eye + yd = -dot ya eye + zd = dot za eye + +-- | Build a matrix for a symmetric perspective-view frustum +perspective + :: Floating a + => a -- ^ FOV (y direction, in radians) + -> a -- ^ Aspect ratio + -> a -- ^ Near plane + -> a -- ^ Far plane + -> M44 a +perspective fovy aspect near far = + V4 (V4 x 0 0 0) + (V4 0 y 0 0) + (V4 0 0 z w) + (V4 0 0 (-1) 0) + where tanHalfFovy = tan $ fovy / 2 + x = 1 / (aspect * tanHalfFovy) + y = 1 / tanHalfFovy + fpn = far + near + fmn = far - near + oon = 0.5/near + oof = 0.5/far + -- z = 1 / (near/fpn - far/fpn) -- would be better by .5 bits + z = -fpn/fmn + w = 1/(oof-oon) -- 13 bits error reduced to 0.17 + -- w = -(2 * far * near) / fmn + +#ifdef HERBIE +{-# ANN perspective "NoHerbie" #-} +#endif + +-- | Build an inverse perspective matrix +inversePerspective + :: Floating a + => a -- ^ FOV (y direction, in radians) + -> a -- ^ Aspect ratio + -> a -- ^ Near plane + -> a -- ^ Far plane + -> M44 a +inversePerspective fovy aspect near far = + V4 (V4 a 0 0 0 ) + (V4 0 b 0 0 ) + (V4 0 0 0 (-1)) + (V4 0 0 c d ) + where tanHalfFovy = tan $ fovy / 2 + a = aspect * tanHalfFovy + b = tanHalfFovy + c = oon - oof + d = oon + oof + oon = 0.5/near + oof = 0.5/far + + +-- | Build a perspective matrix per the classic @glFrustum@ arguments. +frustum + :: Floating a + => a -- ^ Left + -> a -- ^ Right + -> a -- ^ Bottom + -> a -- ^ Top + -> a -- ^ Near + -> a -- ^ Far + -> M44 a +frustum l r b t n f = + V4 (V4 x 0 a 0) + (V4 0 y e 0) + (V4 0 0 c d) + (V4 0 0 (-1) 0) + where + rml = r-l + tmb = t-b + fmn = f-n + x = 2*n/rml + y = 2*n/tmb + a = (r+l)/rml + e = (t+b)/tmb + c = negate (f+n)/fmn + d = (-2*f*n)/fmn + +inverseFrustum + :: Floating a + => a -- ^ Left + -> a -- ^ Right + -> a -- ^ Bottom + -> a -- ^ Top + -> a -- ^ Near + -> a -- ^ Far + -> M44 a +inverseFrustum l r b t n f = + V4 (V4 rx 0 0 ax) + (V4 0 ry 0 by) + (V4 0 0 0 (-1)) + (V4 0 0 rd cd) + where + hrn = 0.5/n + hrnf = 0.5/(n*f) + rx = (r-l)*hrn + ry = (t-b)*hrn + ax = (r+l)*hrn + by = (t+b)*hrn + cd = (f+n)*hrnf + rd = (n-f)*hrnf + +-- | Build a matrix for a symmetric perspective-view frustum with a far plane at infinite +infinitePerspective + :: Floating a + => a -- ^ FOV (y direction, in radians) + -> a -- ^ Aspect Ratio + -> a -- ^ Near plane + -> M44 a +infinitePerspective fovy a n = + V4 (V4 x 0 0 0) + (V4 0 y 0 0) + (V4 0 0 (-1) w) + (V4 0 0 (-1) 0) + where + t = n*tan(fovy/2) + b = -t + l = b*a + r = t*a + x = (2*n)/(r-l) + y = (2*n)/(t-b) + w = -2*n + +inverseInfinitePerspective + :: Floating a + => a -- ^ FOV (y direction, in radians) + -> a -- ^ Aspect Ratio + -> a -- ^ Near plane + -> M44 a +inverseInfinitePerspective fovy a n = + V4 (V4 rx 0 0 0) + (V4 0 ry 0 0) + (V4 0 0 0 (-1)) + (V4 0 0 rw (-rw)) + where + t = n*tan(fovy/2) + b = -t + l = b*a + r = t*a + hrn = 0.5/n + rx = (r-l)*hrn + ry = (t-b)*hrn + rw = -hrn + +-- | Build an orthographic perspective matrix from 6 clipping planes. +-- This matrix takes the region delimited by these planes and maps it +-- to normalized device coordinates between [-1,1] +-- +-- This call is designed to mimic the parameters to the OpenGL @glOrtho@ +-- call, so it has a slightly strange convention: Notably: the near and +-- far planes are negated. +-- +-- Consequently: +-- +-- @ +-- 'ortho' l r b t n f !* 'V4' l b (-n) 1 = 'V4' (-1) (-1) (-1) 1 +-- 'ortho' l r b t n f !* 'V4' r t (-f) 1 = 'V4' 1 1 1 1 +-- @ +-- +-- Examples: +-- +-- >>> ortho 1 2 3 4 5 6 !* V4 1 3 (-5) 1 +-- V4 (-1.0) (-1.0) (-1.0) 1.0 +-- +-- >>> ortho 1 2 3 4 5 6 !* V4 2 4 (-6) 1 +-- V4 1.0 1.0 1.0 1.0 +ortho + :: Fractional a + => a -- ^ Left + -> a -- ^ Right + -> a -- ^ Bottom + -> a -- ^ Top + -> a -- ^ Near + -> a -- ^ Far + -> M44 a +ortho l r b t n f = + V4 (V4 (-2*x) 0 0 ((r+l)*x)) + (V4 0 (-2*y) 0 ((t+b)*y)) + (V4 0 0 (2*z) ((f+n)*z)) + (V4 0 0 0 1) + where x = recip(l-r) + y = recip(b-t) + z = recip(n-f) + +-- | Build an inverse orthographic perspective matrix from 6 clipping planes +inverseOrtho + :: Fractional a + => a -- ^ Left + -> a -- ^ Right + -> a -- ^ Bottom + -> a -- ^ Top + -> a -- ^ Near + -> a -- ^ Far + -> M44 a +inverseOrtho l r b t n f = + V4 (V4 x 0 0 c) + (V4 0 y 0 d) + (V4 0 0 z e) + (V4 0 0 0 1) + where x = 0.5*(r-l) + y = 0.5*(t-b) + z = 0.5*(n-f) + c = 0.5*(l+r) + d = 0.5*(b+t) + e = -0.5*(n+f) diff --git a/src/Linear/Quaternion.hs b/src/Linear/Quaternion.hs --- a/src/Linear/Quaternion.hs +++ b/src/Linear/Quaternion.hs @@ -1,8 +1,18 @@ -{-# LANGUAGE DeriveDataTypeable, PatternGuards, ScopedTypeVariables #-} +{-# LANGUAGE DeriveDataTypeable #-} +{-# LANGUAGE PatternGuards #-} +{-# LANGUAGE ScopedTypeVariables #-} +{-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE MultiParamTypeClasses #-} +{-# LANGUAGE CPP #-} +{-# LANGUAGE TypeFamilies #-} +{-# LANGUAGE Trustworthy #-} +{-# LANGUAGE DeriveGeneric #-} +{-# LANGUAGE DataKinds #-} +{-# LANGUAGE DeriveLift #-} + ----------------------------------------------------------------------------- -- | --- Module : Linear.Quaternion --- Copyright : (C) 2012-2013 Edward Kmett, +-- Copyright : (C) 2012-2015 Edward Kmett -- License : BSD-style (see the file LICENSE) -- -- Maintainer : Edward Kmett @@ -15,6 +25,7 @@ ( Quaternion(..) , Complicated(..) , Hamiltonian(..) + , ee, ei, ej, ek , slerp , asinq , acosq @@ -29,31 +40,82 @@ ) where import Control.Applicative +import Control.DeepSeq (NFData(rnf)) +import Control.Monad (liftM) +import Control.Monad.Fix +import Control.Monad.Zip +import Control.Lens as Lens hiding ((<.>)) +import Data.Binary as Binary +import Data.Bytes.Serial import Data.Complex (Complex((:+))) import Data.Data import Data.Distributive -import Data.Traversable import Data.Foldable +import qualified Data.Foldable.WithIndex as WithIndex import Data.Functor.Bind +import Data.Functor.Classes +import Data.Functor.Rep +import qualified Data.Functor.WithIndex as WithIndex +import Data.Hashable +import Data.Hashable.Lifted +#if !(MIN_VERSION_base(4,11,0)) +import Data.Semigroup (Semigroup(..)) +#endif +import Data.Serialize as Cereal import GHC.Arr (Ix(..)) import qualified Data.Foldable as F -import Data.Monoid +import qualified Data.Traversable.WithIndex as WithIndex +import qualified Data.Vector as V +import qualified Data.Vector.Generic.Mutable as M +import qualified Data.Vector.Generic as G +import qualified Data.Vector.Unboxed.Base as U import Foreign.Ptr (castPtr, plusPtr) import Foreign.Storable (Storable(..)) -import Linear.Core +import GHC.Generics (Generic, Generic1) +#if defined(MIN_VERSION_template_haskell) +import Language.Haskell.TH.Syntax (Lift) +#endif import Linear.Epsilon import Linear.Conjugate import Linear.Metric +import Linear.V +import Linear.V2 import Linear.V3 +import Linear.V4 import Linear.Vector import Prelude hiding (any) - -{-# ANN module "HLint: ignore Reduce duplication" #-} +import System.Random (Random(..), Uniform) +import System.Random.Stateful (UniformRange(..)) -- | Quaternions -data Quaternion a = Quaternion a {-# UNPACK #-}!(V3 a) - deriving (Eq,Ord,Read,Show,Data,Typeable) +data Quaternion a = Quaternion !a {-# UNPACK #-}!(V3 a) + deriving (Eq,Ord,Read,Show,Data + ,Generic,Generic1 +#if defined(MIN_VERSION_template_haskell) + ,Lift +#endif + ) +instance Finite Quaternion where + type Size Quaternion = 4 + toV (Quaternion a (V3 b c d)) = V (V.fromListN 4 [a, b, c, d]) + fromV (V v) = Quaternion (v V.! 0) (V3 (v V.! 1) (v V.! 2) (v V.! 3)) + +instance Random a => Random (Quaternion a) where + random g = case random g of + (a, g') -> case random g' of + (b, g'') -> (Quaternion a b, g'') + randomR (Quaternion a b, Quaternion c d) g = case randomR (a,c) g of + (e, g') -> case randomR (b,d) g' of + (f, g'') -> (Quaternion e f, g'') + +instance Uniform a => Uniform (Quaternion a) where + +instance UniformRange a => UniformRange (Quaternion a) where + uniformRM (Quaternion a b, Quaternion c d) g = Quaternion + <$> uniformRM (a, c) g + <*> uniformRM (b, d) g + instance Functor Quaternion where fmap f (Quaternion e v) = Quaternion (f e) (fmap f v) {-# INLINE fmap #-} @@ -70,7 +132,13 @@ Quaternion f fv <*> Quaternion a v = Quaternion (f a) (fv <*> v) {-# INLINE (<*>) #-} -instance Additive Quaternion +instance Additive Quaternion where + zero = pure 0 + {-# INLINE zero #-} + liftU2 = liftA2 + {-# INLINE liftU2 #-} + liftI2 = liftA2 + {-# INLINE liftI2 #-} instance Bind Quaternion where Quaternion a (V3 b c d) >>- f = Quaternion a' (V3 b' c' d') where @@ -106,15 +174,49 @@ inRange (l1,u1) i1 && inRange (l2,u2) i2 {-# INLINE inRange #-} -instance Core Quaternion where - core f = Quaternion (f _e) (V3 (f _i) (f _j) (f _k)) - {-# INLINE core #-} +instance Representable Quaternion where + type Rep Quaternion = E Quaternion + tabulate f = Quaternion (f ee) (V3 (f ei) (f ej) (f ek)) + {-# INLINE tabulate #-} + index xs (E l) = view l xs + {-# INLINE index #-} +instance WithIndex.FunctorWithIndex (E Quaternion) Quaternion where + imap f (Quaternion a (V3 b c d)) = Quaternion (f ee a) $ V3 (f ei b) (f ej c) (f ek d) + {-# INLINE imap #-} + +instance WithIndex.FoldableWithIndex (E Quaternion) Quaternion where + ifoldMap f (Quaternion a (V3 b c d)) = f ee a `mappend` f ei b `mappend` f ej c `mappend` f ek d + {-# INLINE ifoldMap #-} + +instance WithIndex.TraversableWithIndex (E Quaternion) Quaternion where + itraverse f (Quaternion a (V3 b c d)) = Quaternion <$> f ee a <*> (V3 <$> f ei b <*> f ej c <*> f ek d) + {-# INLINE itraverse #-} + +#if !MIN_VERSION_lens(5,0,0) +instance Lens.FunctorWithIndex (E Quaternion) Quaternion where imap = WithIndex.imap +instance Lens.FoldableWithIndex (E Quaternion) Quaternion where ifoldMap = WithIndex.ifoldMap +instance Lens.TraversableWithIndex (E Quaternion) Quaternion where itraverse = WithIndex.itraverse +#endif + +type instance Index (Quaternion a) = E Quaternion +type instance IxValue (Quaternion a) = a + +instance Ixed (Quaternion a) where + ix i = el i + {-# INLINE ix #-} + +instance Each (Quaternion a) (Quaternion b) a b where + each = traverse + {-# INLINE each #-} + instance Foldable Quaternion where foldMap f (Quaternion e v) = f e `mappend` foldMap f v {-# INLINE foldMap #-} foldr f z (Quaternion e v) = f e (F.foldr f z v) {-# INLINE foldr #-} + null _ = False + length _ = 4 instance Traversable Quaternion where traverse f (Quaternion e v) = Quaternion <$> f e <*> traverse f v @@ -167,6 +269,14 @@ ik = isInfinite k {-# INLINE signum #-} +instance Hashable a => Hashable (Quaternion a) where + hashWithSalt s (Quaternion a b) = s `hashWithSalt` a `hashWithSalt` b + {-# INLINE hashWithSalt #-} + +instance Hashable1 Quaternion where + liftHashWithSalt h s (Quaternion a b) = liftHashWithSalt h (h s a) b + {-# INLINE liftHashWithSalt #-} + qNaN :: RealFloat a => Quaternion a qNaN = Quaternion fNaN (V3 fNaN fNaN fNaN) where fNaN = 0/0 {-# INLINE qNaN #-} @@ -186,7 +296,7 @@ (r0*q3-r1*q2+r2*q1-r3*q0)) ^/ (r0*r0 + r1*r1 + r2*r2 + r3*r3) {-# INLINE (/) #-} - recip q = q ^/ quadrance q + recip q@(Quaternion e v) = Quaternion e (negate v) ^/ quadrance q {-# INLINE recip #-} fromRational x = Quaternion (fromRational x) 0 {-# INLINE fromRational #-} @@ -197,17 +307,12 @@ -- | A vector space that includes the basis elements '_e' and '_i' class Complicated t where - -- | - -- @ - -- '_e' :: Lens' (t a) a - -- @ - _e :: Functor f => (a -> f a) -> t a -> f (t a) - -- | - -- @ - -- '_i' :: Lens' (t a) a - -- @ - _i :: Functor f => (a -> f a) -> t a -> f (t a) + _e, _i :: Lens' (t a) a +ee, ei :: Complicated t => E t +ee = E _e +ei = E _i + instance Complicated Complex where _e f (a :+ b) = (:+ b) <$> f a {-# INLINE _e #-} @@ -222,22 +327,13 @@ -- | A vector space that includes the basis elements '_e', '_i', '_j' and '_k' class Complicated t => Hamiltonian t where - -- | - -- @ - -- '_j' :: Lens' (t a) a - -- @ - _j :: Functor f => (a -> f a) -> t a -> f (t a) - -- | - -- @ - -- '_k' :: Lens' (t a) a - -- @ - _k :: Functor f => (a -> f a) -> t a -> f (t a) - -- | - -- @ - -- '_ijk' :: Lens' (t a) (V3 a) - -- @ - _ijk :: Functor f => (V3 a -> f (V3 a)) -> t a -> f (t a) + _j, _k :: Lens' (t a) a + _ijk :: Lens' (t a) (V3 a) +ej, ek :: Hamiltonian t => E t +ej = E _j +ek = E _k + instance Hamiltonian Quaternion where _j f (Quaternion a v) = Quaternion a <$> _y f v {-# INLINE _j #-} @@ -280,6 +376,29 @@ pow q t = exp (t *^ log q) {-# INLINE pow #-} +sqrte2pqiq :: (Floating a, Ord a) => a -> a -> a +sqrte2pqiq e qiq -- = sqrt (e*e + qiq) + | e < - 1.5097698010472593e153 = -(qiq/e) - e + | e < 5.582399551122541e57 = sqrt (e*e + qiq) -- direct definition + | otherwise = (qiq/e) + e +-- {-# SPECIALIZE sqrte2pqiq :: Double -> Double -> Double #-} +-- {-# SPECIALIZE sqrte2pqiq :: Float -> Float -> Float #-} +#ifdef HERBIE +{-# ANN sqrte2pqiq "NoHerbie" #-} +#endif + +tanrhs :: (Floating a, Ord a) => a -> a -> a -> a +tanrhs sai ai d -- = cosh ai * (sai / ai) / d -- improved from 6.04 bits of error to 0.19 bits + | sai < -4.618902267687042e-52 = (sai / d / ai) * cosh ai + | sai < 1.038530535935153e-39 = (cosh ai * sai) / ai / d + | otherwise = (sai / d / ai) * cosh ai +-- {-# SPECIALIZE tanrhs :: Double -> Double -> Double -> Double #-} +-- {-# SPECIALIZE tanrhs :: Float -> Float -> Float -> Float #-} +#ifdef HERBIE +{-# ANN tanrhs "NoHerbie" #-} +#endif + + -- ehh.. instance RealFloat a => Floating (Quaternion a) where {-# SPECIALIZE instance Floating (Quaternion Float) #-} @@ -288,18 +407,21 @@ {-# INLINE pi #-} exp q@(Quaternion e v) | qiq == 0 = Quaternion (exp e) v - | ai <- sqrt qiq, ee <- exp e = reimagine (ee * cos ai) (ee * (sin ai / ai)) q + | ai <- sqrt qiq, exe <- exp e = reimagine (exe * cos ai) (exe * (sin ai / ai)) q where qiq = qi q {-# INLINE exp #-} - log q@(Quaternion e v@(V3 _i j k)) + log q@(Quaternion e v) | qiq == 0 = if e >= 0 - then Quaternion (log e) v - else Quaternion (log (negate e)) (V3 pi j k) -- mmm, pi - | ai <- sqrt qiq, m <- sqrt (e*e + qiq) = reimagine (log m) (atan2 m e / ai) q + then Quaternion (log e) v -- Using v rather than 0 preserves negative zeros + else Quaternion (negate (log (negate e))) v -- negative scalar: negate quaternion, take log, negate again, preserves negative zeros + | ai <- sqrt qiq = reimagine (log m) (acos (e / m) / ai) q where qiq = qi q + m = sqrte2pqiq e qiq {-# INLINE log #-} + x ** y = exp (y * log x) {-# INLINE (**) #-} + sqrt q@(Quaternion e v) | m == 0 = q | qiq == 0 = if e > 0 @@ -307,38 +429,44 @@ else Quaternion 0 (V3 (sqrt (negate e)) 0 0) | im <- sqrt (0.5*(m-e)) / sqrt qiq = Quaternion (0.5*(m+e)) (v^*im) where qiq = qi q - m = sqrt (e*e + qiq) + m = sqrte2pqiq e qiq {-# INLINE sqrt #-} + cos q@(Quaternion e v) | qiq == 0 = Quaternion (cos e) v - | ai <- sqrt qiq = reimagine (cos e * cosh ai) (- sin e * (sinh ai / ai)) q + | ai <- sqrt qiq = reimagine (cos e * cosh ai) (- sin e / ai / sinh ai) q -- 0.15 bits error where qiq = qi q {-# INLINE cos #-} + sin q@(Quaternion e v) | qiq == 0 = Quaternion (sin e) v - | ai <- sqrt qiq = reimagine (sin e * cosh ai) (cos e * (sinh ai / ai)) q + | ai <- sqrt qiq = reimagine (sin e * cosh ai) (cos e * sinh ai / ai) q where qiq = qi q {-# INLINE sin #-} + tan q@(Quaternion e v) | qiq == 0 = Quaternion (tan e) v | ai <- sqrt qiq, ce <- cos e, sai <- sinh ai, d <- ce*ce + sai*sai = - reimagine (ce * sin e / d) (cosh ai * (sai / ai) / d) q + reimagine (ce * sin e / d) (tanrhs sai ai d) q where qiq = qi q {-# INLINE tan #-} + sinh q@(Quaternion e v) | qiq == 0 = Quaternion (sinh e) v - | ai <- sqrt qiq = reimagine (sinh e * cos ai) (cosh e * (sin ai / ai)) q + | ai <- sqrt qiq = reimagine (sinh e * cos ai) (cosh e * sin ai / ai) q where qiq = qi q {-# INLINE sinh #-} + cosh q@(Quaternion e v) | qiq == 0 = Quaternion (cosh e) v - | ai <- sqrt qiq = reimagine (cosh e * cos ai) ((sinh e * sin ai) / ai) q + | ai <- sqrt qiq = reimagine (cosh e * cos ai) (sin ai * (sinh e / ai)) q where qiq = qi q {-# INLINE cosh #-} + tanh q@(Quaternion e v) | qiq == 0 = Quaternion (tanh e) v | ai <- sqrt qiq, se <- sinh e, cai <- cos ai, d <- se*se + cai*cai = - reimagine ((cosh e * se) / d) ((cai * (sin ai / ai)) / d) q + reimagine (cosh e * se / d) (tanhrhs cai ai d) q where qiq = qi q {-# INLINE tanh #-} @@ -356,6 +484,15 @@ atanh = cut atanh {-# INLINE atanh #-} +tanhrhs :: (Floating a, Ord a) => a -> a -> a -> a +tanhrhs cai ai d -- = cai * (sin ai / ai) / d + | d >= -4.2173720203427147e-29 && d < 4.446702369113811e64 = cai / (d * (ai / sin ai)) + | otherwise = cai * (1 / ai / sin ai) / d +-- {-# SPECIALIZE tanhrhs :: Double -> Double -> Double -> Double #-} +-- {-# SPECIALIZE tanhrhs :: Float -> Float -> Float -> Float #-} +#ifdef HERBIE +{-# ANN tanhrhs "NoHerbie" #-} +#endif -- | Helper for calculating with specific branch cuts cut :: RealFloat a => (Complex a -> Complex a) -> Quaternion a -> Quaternion a @@ -424,14 +561,15 @@ {-# INLINE atanhq #-} -- | Spherical linear interpolation between two quaternions. + slerp :: RealFloat a => Quaternion a -> Quaternion a -> a -> Quaternion a slerp q p t | 1.0 - cosphi < 1e-8 = q - | phi <- acos cosphi, r <- recip (sin phi) - = (sin ((1-t)*phi)*r *^ q ^+^ f (sin (t*phi)*r) *^ p) ^/ sin phi + | otherwise = ((sin ((1-t)*phi) *^ q) + sin (t*phi) *^ f p) ^/ sin phi where - dqp = dot q p - (cosphi, f) = if dqp < 0 then (-dqp, negate) else (dqp, id) + dqp = dot q p + (cosphi, f) = if dqp < 0 then (-dqp, negate) else (dqp, id) + phi = acos cosphi {-# SPECIALIZE slerp :: Quaternion Float -> Quaternion Float -> Float -> Quaternion Float #-} {-# SPECIALIZE slerp :: Quaternion Double -> Quaternion Double -> Double -> Quaternion Double #-} @@ -449,6 +587,117 @@ -- | @'axisAngle' axis theta@ builds a 'Quaternion' representing a -- rotation of @theta@ radians about @axis@. axisAngle :: (Epsilon a, Floating a) => V3 a -> a -> Quaternion a -axisAngle axis theta = normalize $ Quaternion (cos half) $ sin half *^ axis +axisAngle axis theta = Quaternion (cos half) (sin half *^ normalize axis) where half = theta / 2 {-# INLINE axisAngle #-} + +data instance U.Vector (Quaternion a) = V_Quaternion !Int (U.Vector a) +data instance U.MVector s (Quaternion a) = MV_Quaternion !Int (U.MVector s a) +instance U.Unbox a => U.Unbox (Quaternion a) + +instance U.Unbox a => M.MVector U.MVector (Quaternion a) where + basicLength (MV_Quaternion n _) = n + basicUnsafeSlice m n (MV_Quaternion _ v) = MV_Quaternion n (M.basicUnsafeSlice (4*m) (4*n) v) + basicOverlaps (MV_Quaternion _ v) (MV_Quaternion _ u) = M.basicOverlaps v u + basicUnsafeNew n = liftM (MV_Quaternion n) (M.basicUnsafeNew (4*n)) + basicUnsafeRead (MV_Quaternion _ v) i = + do let o = 4*i + x <- M.basicUnsafeRead v o + y <- M.basicUnsafeRead v (o+1) + z <- M.basicUnsafeRead v (o+2) + w <- M.basicUnsafeRead v (o+3) + return (Quaternion x (V3 y z w)) + basicUnsafeWrite (MV_Quaternion _ v) i (Quaternion x (V3 y z w)) = + do let o = 4*i + M.basicUnsafeWrite v o x + M.basicUnsafeWrite v (o+1) y + M.basicUnsafeWrite v (o+2) z + M.basicUnsafeWrite v (o+3) w + basicInitialize (MV_Quaternion _ v) = M.basicInitialize v + +instance U.Unbox a => G.Vector U.Vector (Quaternion a) where + basicUnsafeFreeze (MV_Quaternion n v) = liftM ( V_Quaternion n) (G.basicUnsafeFreeze v) + basicUnsafeThaw ( V_Quaternion n v) = liftM (MV_Quaternion n) (G.basicUnsafeThaw v) + basicLength ( V_Quaternion n _) = n + basicUnsafeSlice m n (V_Quaternion _ v) = V_Quaternion n (G.basicUnsafeSlice (4*m) (4*n) v) + basicUnsafeIndexM (V_Quaternion _ v) i = + do let o = 4*i + x <- G.basicUnsafeIndexM v o + y <- G.basicUnsafeIndexM v (o+1) + z <- G.basicUnsafeIndexM v (o+2) + w <- G.basicUnsafeIndexM v (o+3) + return (Quaternion x (V3 y z w)) + +instance MonadZip Quaternion where + mzipWith = liftA2 + +instance MonadFix Quaternion where + mfix f = Quaternion (let Quaternion a _ = f a in a) + (V3 (let Quaternion _ (V3 a _ _) = f a in a) + (let Quaternion _ (V3 _ a _) = f a in a) + (let Quaternion _ (V3 _ _ a) = f a in a)) + +instance NFData a => NFData (Quaternion a) where + rnf (Quaternion a b) = rnf a `seq` rnf b + +instance Serial1 Quaternion where + serializeWith f (Quaternion a b) = f a >> serializeWith f b + deserializeWith f = Quaternion <$> f <*> deserializeWith f + +instance Serial a => Serial (Quaternion a) where + serialize = serializeWith serialize + deserialize = deserializeWith deserialize + +instance Binary a => Binary (Quaternion a) where + put = serializeWith Binary.put + get = deserializeWith Binary.get + +instance Serialize a => Serialize (Quaternion a) where + put = serializeWith Cereal.put + get = deserializeWith Cereal.get + +instance Eq1 Quaternion where + liftEq f (Quaternion a b) (Quaternion c d) = f a c && liftEq f b d +instance Ord1 Quaternion where + liftCompare f (Quaternion a b) (Quaternion c d) = f a c `mappend` liftCompare f b d +instance Show1 Quaternion where + liftShowsPrec f g d (Quaternion a b) = showsBinaryWith f (liftShowsPrec f g) "Quaternion" d a b +instance Read1 Quaternion where + liftReadsPrec f g = readsData $ readsBinaryWith f (liftReadsPrec f g) "Quaternion" Quaternion + +instance Field1 (Quaternion a) (Quaternion a) a a where + _1 f (Quaternion w xyz) = f w <&> \w' -> Quaternion w' xyz + +instance Field2 (Quaternion a) (Quaternion a) a a where + _2 f (Quaternion w (V3 x y z)) = f x <&> \x' -> Quaternion w (V3 x' y z) + +instance Field3 (Quaternion a) (Quaternion a) a a where + _3 f (Quaternion w (V3 x y z)) = f y <&> \y' -> Quaternion w (V3 x y' z) + +instance Field4 (Quaternion a) (Quaternion a) a a where + _4 f (Quaternion w (V3 x y z)) = f z <&> \z' -> Quaternion w (V3 x y z') + +instance Semigroup a => Semigroup (Quaternion a) where + (<>) = liftA2 (<>) + +instance Monoid a => Monoid (Quaternion a) where + mempty = pure mempty +#if !(MIN_VERSION_base(4,11,0)) + mappend = liftA2 mappend +#endif + +instance R1 Quaternion where + _x f (Quaternion w (V3 x y z)) = f x <&> \x' -> Quaternion w (V3 x' y z) + +instance R2 Quaternion where + _y f (Quaternion w (V3 x y z)) = f y <&> \y' -> Quaternion w (V3 x y' z) + _xy f (Quaternion w (V3 x y z)) = f (V2 x y) <&> \(V2 x' y') -> Quaternion w (V3 x' y' z) + +instance R3 Quaternion where + _z f (Quaternion w (V3 x y z)) = f z <&> \z' -> Quaternion w (V3 x y z') + _xyz f (Quaternion w xyz) = Quaternion w <$> f xyz + +instance R4 Quaternion where + _w f (Quaternion w xyz) = f w <&> \w' -> Quaternion w' xyz + _xyzw f (Quaternion w (V3 x y z)) = f (V4 x y z w) <&> \(V4 x' y' z' w') -> Quaternion w' (V3 x' y' z') + diff --git a/src/Linear/Trace.hs b/src/Linear/Trace.hs new file mode 100644 --- /dev/null +++ b/src/Linear/Trace.hs @@ -0,0 +1,116 @@ +{-# LANGUAGE CPP #-} +{-# LANGUAGE TypeOperators #-} +{-# LANGUAGE DefaultSignatures #-} +{-# LANGUAGE PolyKinds #-} +{-# LANGUAGE Trustworthy #-} +--------------------------------------------------------------------------- +-- | +-- Copyright : (C) 2012-2015 Edward Kmett +-- License : BSD-style (see the file LICENSE) +-- +-- Maintainer : Edward Kmett +-- Stability : experimental +-- Portability : non-portable +-- +-- Simple matrix operation for low-dimensional primitives. +--------------------------------------------------------------------------- +module Linear.Trace + ( Trace(..) + , frobenius + ) where + +import Control.Monad as Monad +import Linear.V0 +import Linear.V1 +import Linear.V2 +import Linear.V3 +import Linear.V4 +import Linear.Plucker +import Linear.Quaternion +import Linear.V +import Linear.Vector +import Data.Complex +import Data.Distributive +import Data.Foldable as Foldable +import Data.Functor.Bind as Bind +import Data.Functor.Compose +import Data.Functor.Product +import Data.Hashable +import Data.HashMap.Lazy +import Data.IntMap (IntMap) +import Data.Map (Map) + +-- $setup +-- >>> import Data.Complex +-- >>> import Debug.SimpleReflect.Vars +-- >>> import Linear.V2 + +class Functor m => Trace m where + -- | Compute the trace of a matrix + -- + -- >>> trace (V2 (V2 a b) (V2 c d)) + -- a + d + trace :: Num a => m (m a) -> a +#ifndef HLINT + default trace :: (Foldable m, Num a) => m (m a) -> a + trace = Foldable.sum . diagonal + {-# INLINE trace #-} +#endif + + -- | Compute the diagonal of a matrix + -- + -- >>> diagonal (V2 (V2 a b) (V2 c d)) + -- V2 a d + diagonal :: m (m a) -> m a +#ifndef HLINT + default diagonal :: Monad m => m (m a) -> m a + diagonal = Monad.join + {-# INLINE diagonal #-} +#endif + +instance Trace IntMap where + diagonal = Bind.join + {-# INLINE diagonal #-} + +instance Ord k => Trace (Map k) where + diagonal = Bind.join + {-# INLINE diagonal #-} + +instance (Eq k, Hashable k) => Trace (HashMap k) where + diagonal = Bind.join + {-# INLINE diagonal #-} + +instance Dim n => Trace (V n) +instance Trace V0 +instance Trace V1 +instance Trace V2 +instance Trace V3 +instance Trace V4 +instance Trace Plucker +instance Trace Quaternion + +instance Trace Complex where + trace ((a :+ _) :+ (_ :+ b)) = a + b + {-# INLINE trace #-} + diagonal ((a :+ _) :+ (_ :+ b)) = a :+ b + {-# INLINE diagonal #-} + +instance (Trace f, Trace g) => Trace (Product f g) where + trace (Pair xx yy) = trace (pfst <$> xx) + trace (psnd <$> yy) where + pfst (Pair x _) = x + psnd (Pair _ y) = y + {-# INLINE trace #-} + diagonal (Pair xx yy) = diagonal (pfst <$> xx) `Pair` diagonal (psnd <$> yy) where + pfst (Pair x _) = x + psnd (Pair _ y) = y + {-# INLINE diagonal #-} + +instance (Distributive g, Trace g, Trace f) => Trace (Compose g f) where + trace = trace . fmap (fmap trace . distribute) . getCompose . fmap getCompose + {-# INLINE trace #-} + diagonal = Compose . fmap diagonal . diagonal . fmap distribute . getCompose . fmap getCompose + {-# INLINE diagonal #-} + +-- | Compute the of a matrix. +frobenius :: (Num a, Foldable f, Additive f, Additive g, Distributive g, Trace g) => f (g a) -> a +frobenius m = trace $ fmap (\ f' -> Foldable.foldl' (^+^) zero $ liftI2 (*^) f' m) (distribute m) diff --git a/src/Linear/V.hs b/src/Linear/V.hs new file mode 100644 --- /dev/null +++ b/src/Linear/V.hs @@ -0,0 +1,594 @@ +{-# LANGUAGE CPP #-} +{-# LANGUAGE TypeOperators #-} +{-# LANGUAGE KindSignatures #-} +{-# LANGUAGE ScopedTypeVariables #-} +{-# LANGUAGE GeneralizedNewtypeDeriving #-} +{-# LANGUAGE DefaultSignatures #-} +{-# LANGUAGE Rank2Types #-} +{-# LANGUAGE TypeFamilies #-} +{-# LANGUAGE EmptyDataDecls #-} +{-# LANGUAGE MultiParamTypeClasses, FlexibleContexts, FlexibleInstances, UndecidableInstances #-} +{-# LANGUAGE DeriveDataTypeable #-} +{-# LANGUAGE DataKinds #-} +{-# LANGUAGE PolyKinds #-} +{-# LANGUAGE RoleAnnotations #-} +{-# LANGUAGE Trustworthy #-} +{-# LANGUAGE DeriveGeneric #-} + +----------------------------------------------------------------------------- +-- | +-- Copyright : (C) 2012-2015 Edward Kmett +-- License : BSD-style (see the file LICENSE) +-- +-- Maintainer : Edward Kmett +-- Stability : experimental +-- Portability : non-portable +-- +-- n-D Vectors +---------------------------------------------------------------------------- + +module Linear.V + ( V(V,toVector) +#ifdef MIN_VERSION_template_haskell + , int +#endif + , dim + , Dim(..) + , reifyDim + , reifyVector + , reifyDimNat + , reifyVectorNat + , fromVector + , Finite(..) + , _V, _V' + ) where + +import Control.Applicative +import Control.DeepSeq (NFData) +import Control.Monad +import Control.Monad.Fix +import Control.Monad.Trans.State +import Control.Monad.Zip +import Control.Lens as Lens +import Data.Binary as Binary +import Data.Bytes.Serial +import Data.Complex +import Data.Data +import Data.Distributive +import Data.Foldable as Foldable +import qualified Data.Foldable.WithIndex as WithIndex +import Data.Functor.Bind +import Data.Functor.Classes +import Data.Functor.Rep as Rep +import qualified Data.Functor.WithIndex as WithIndex +import Data.Hashable +import Data.Hashable.Lifted +import Data.Kind +import Data.Reflection as R +import Data.Serialize as Cereal +import qualified Data.Traversable.WithIndex as WithIndex +import qualified Data.Vector as V +import Data.Vector (Vector) +import Data.Vector.Fusion.Util (Box(..)) +import qualified Data.Vector.Generic as G +import qualified Data.Vector.Unboxed as U +import qualified Data.Vector.Generic.Mutable as M +import Foreign.Ptr +import Foreign.Storable +import GHC.TypeLits +import GHC.Generics (Generic, Generic1) +#if !(MIN_VERSION_reflection(1,3,0)) && defined(MIN_VERSION_template_haskell) +import Language.Haskell.TH +#endif +import Linear.Epsilon +import Linear.Metric +import Linear.Vector +import Prelude as P +#if !(MIN_VERSION_base(4,11,0)) +import Data.Semigroup +#endif +import System.Random (Random(..)) +import System.Random.Stateful (Uniform(..), UniformRange(..)) + +class Dim n where + reflectDim :: p n -> Int + +type role V nominal representational + +class Finite v where + type Size (v :: Type -> Type) :: Nat -- this should allow kind k, for Reifies k Int + toV :: v a -> V (Size v) a + default toV :: Foldable v => v a -> V (Size v) a + toV = V . V.fromList . Foldable.toList + fromV :: V (Size v) a -> v a + +instance Finite Complex where + type Size Complex = 2 + toV (a :+ b) = V (V.fromListN 2 [a, b]) + fromV (V v) = (v V.! 0) :+ (v V.! 1) + +_V :: (Finite u, Finite v) => Iso (V (Size u) a) (V (Size v) b) (u a) (v b) +_V = iso fromV toV + +_V' :: Finite v => Iso (V (Size v) a) (V (Size v) b) (v a) (v b) +_V' = iso fromV toV + +instance Finite (V (n :: Nat)) where + type Size (V n) = n + toV = id + fromV = id + +newtype V n a = V { toVector :: V.Vector a } deriving (Eq,Ord,Show,Read,NFData + ,Generic,Generic1 + ) + +dim :: forall n a. Dim n => V n a -> Int +dim _ = reflectDim (Proxy :: Proxy n) +{-# INLINE dim #-} + +instance KnownNat n => Dim (n :: Nat) where + reflectDim = fromInteger . natVal + {-# INLINE reflectDim #-} + +instance (Dim n, Random a) => Random (V n a) where + random = runState (V <$> V.replicateM (reflectDim (Proxy :: Proxy n)) (state random)) + randomR (V ls,V hs) = runState (V <$> V.zipWithM (\l h -> state $ randomR (l,h)) ls hs) + +instance (Dim n, Uniform a) => Uniform (V n a) where + uniformM g = V <$> V.replicateM (reflectDim (Proxy :: Proxy n)) (uniformM g) + +instance (Dim n, UniformRange a) => UniformRange (V n a) where + uniformRM (V ls, V hs) g = V <$> V.zipWithM (\l h -> uniformRM (l, h) g) ls hs +#if (MIN_VERSION_random(1,3,0)) + isInRange (V ls, V hs) (V xs) = V.and $ V.zipWith3 (\l h x -> isInRange (l, h) x) ls hs xs +#endif + +data ReifiedDim (s :: Type) + +retagDim :: (Proxy s -> a) -> proxy (ReifiedDim s) -> a +retagDim f _ = f Proxy +{-# INLINE retagDim #-} + +instance Reifies s Int => Dim (ReifiedDim s) where + reflectDim = retagDim reflect + {-# INLINE reflectDim #-} + +reifyDimNat :: Int -> (forall (n :: Nat). KnownNat n => Proxy n -> r) -> r +reifyDimNat i f = R.reifyNat (fromIntegral i) f +{-# INLINE reifyDimNat #-} + +reifyVectorNat :: forall a r. Vector a -> (forall (n :: Nat). KnownNat n => V n a -> r) -> r +reifyVectorNat v f = reifyNat (fromIntegral $ V.length v) $ \(Proxy :: Proxy n) -> f (V v :: V n a) +{-# INLINE reifyVectorNat #-} + +reifyDim :: Int -> (forall (n :: Type). Dim n => Proxy n -> r) -> r +reifyDim i f = R.reify i (go f) where + go :: (Proxy (ReifiedDim n) -> a) -> proxy n -> a + go g _ = g Proxy +{-# INLINE reifyDim #-} + +reifyVector :: forall a r. Vector a -> (forall (n :: Type). Dim n => V n a -> r) -> r +reifyVector v f = reifyDim (V.length v) $ \(Proxy :: Proxy n) -> f (V v :: V n a) +{-# INLINE reifyVector #-} + +instance Dim n => Dim (V n a) where + reflectDim _ = reflectDim (Proxy :: Proxy n) + {-# INLINE reflectDim #-} + +instance (Dim n, Semigroup a) => Semigroup (V n a) where + (<>) = liftA2 (<>) + +instance (Dim n, Monoid a) => Monoid (V n a) where + mempty = pure mempty +#if !(MIN_VERSION_base(4,11,0)) + mappend = liftA2 mappend +#endif + +instance Functor (V n) where + fmap f (V as) = V (fmap f as) + {-# INLINE fmap #-} + +instance WithIndex.FunctorWithIndex Int (V n) where + imap f (V as) = V (Lens.imap f as) + {-# INLINE imap #-} + +instance Foldable (V n) where + fold (V as) = fold as + {-# INLINE fold #-} + foldMap f (V as) = Foldable.foldMap f as + {-# INLINE foldMap #-} + foldr f z (V as) = V.foldr f z as + {-# INLINE foldr #-} + foldl f z (V as) = V.foldl f z as + {-# INLINE foldl #-} + foldr' f z (V as) = V.foldr' f z as + {-# INLINE foldr' #-} + foldl' f z (V as) = V.foldl' f z as + {-# INLINE foldl' #-} + foldr1 f (V as) = V.foldr1 f as + {-# INLINE foldr1 #-} + foldl1 f (V as) = V.foldl1 f as + {-# INLINE foldl1 #-} + length (V as) = V.length as + {-# INLINE length #-} + null (V as) = V.null as + {-# INLINE null #-} + toList (V as) = V.toList as + {-# INLINE toList #-} + elem a (V as) = V.elem a as + {-# INLINE elem #-} + maximum (V as) = V.maximum as + {-# INLINE maximum #-} + minimum (V as) = V.minimum as + {-# INLINE minimum #-} + sum (V as) = V.sum as + {-# INLINE sum #-} + product (V as) = V.product as + {-# INLINE product #-} + +instance WithIndex.FoldableWithIndex Int (V n) where + ifoldMap f (V as) = ifoldMap f as + {-# INLINE ifoldMap #-} + +instance Traversable (V n) where + traverse f (V as) = V <$> traverse f as + {-# INLINE traverse #-} + +instance WithIndex.TraversableWithIndex Int (V n) where + itraverse f (V as) = V <$> itraverse f as + {-# INLINE itraverse #-} + +#if !MIN_VERSION_lens(5,0,0) +instance Lens.FunctorWithIndex Int (V n) where imap = WithIndex.imap +instance Lens.FoldableWithIndex Int (V n) where ifoldMap = WithIndex.ifoldMap +instance Lens.TraversableWithIndex Int (V n) where itraverse = WithIndex.itraverse +#endif + +instance Apply (V n) where + V as <.> V bs = V (V.zipWith id as bs) + {-# INLINE (<.>) #-} + +instance Dim n => Applicative (V n) where + pure = V . V.replicate (reflectDim (Proxy :: Proxy n)) + {-# INLINE pure #-} + + V as <*> V bs = V (V.zipWith id as bs) + {-# INLINE (<*>) #-} + +instance Bind (V n) where + V as >>- f = V $ V.generate (V.length as) $ \i -> + toVector (f (as `V.unsafeIndex` i)) `V.unsafeIndex` i + {-# INLINE (>>-) #-} + +instance Dim n => Monad (V n) where +#if !(MIN_VERSION_base(4,11,0)) + return = V . V.replicate (reflectDim (Proxy :: Proxy n)) + {-# INLINE return #-} +#endif + V as >>= f = V $ V.generate (reflectDim (Proxy :: Proxy n)) $ \i -> + toVector (f (as `V.unsafeIndex` i)) `V.unsafeIndex` i + {-# INLINE (>>=) #-} + +instance Dim n => Additive (V n) where + zero = pure 0 + {-# INLINE zero #-} + liftU2 f (V as) (V bs) = V (V.zipWith f as bs) + {-# INLINE liftU2 #-} + liftI2 f (V as) (V bs) = V (V.zipWith f as bs) + {-# INLINE liftI2 #-} + +instance (Dim n, Num a) => Num (V n a) where + V as + V bs = V $ V.zipWith (+) as bs + {-# INLINE (+) #-} + V as - V bs = V $ V.zipWith (-) as bs + {-# INLINE (-) #-} + V as * V bs = V $ V.zipWith (*) as bs + {-# INLINE (*) #-} + negate = fmap negate + {-# INLINE negate #-} + abs = fmap abs + {-# INLINE abs #-} + signum = fmap signum + {-# INLINE signum #-} + fromInteger = pure . fromInteger + {-# INLINE fromInteger #-} + +instance (Dim n, Fractional a) => Fractional (V n a) where + recip = fmap recip + {-# INLINE recip #-} + V as / V bs = V $ V.zipWith (/) as bs + {-# INLINE (/) #-} + fromRational = pure . fromRational + {-# INLINE fromRational #-} + +instance (Dim n, Floating a) => Floating (V n a) where + pi = pure pi + {-# INLINE pi #-} + exp = fmap exp + {-# INLINE exp #-} + sqrt = fmap sqrt + {-# INLINE sqrt #-} + log = fmap log + {-# INLINE log #-} + V as ** V bs = V $ V.zipWith (**) as bs + {-# INLINE (**) #-} + logBase (V as) (V bs) = V $ V.zipWith logBase as bs + {-# INLINE logBase #-} + sin = fmap sin + {-# INLINE sin #-} + tan = fmap tan + {-# INLINE tan #-} + cos = fmap cos + {-# INLINE cos #-} + asin = fmap asin + {-# INLINE asin #-} + atan = fmap atan + {-# INLINE atan #-} + acos = fmap acos + {-# INLINE acos #-} + sinh = fmap sinh + {-# INLINE sinh #-} + tanh = fmap tanh + {-# INLINE tanh #-} + cosh = fmap cosh + {-# INLINE cosh #-} + asinh = fmap asinh + {-# INLINE asinh #-} + atanh = fmap atanh + {-# INLINE atanh #-} + acosh = fmap acosh + {-# INLINE acosh #-} + +instance Dim n => Distributive (V n) where + distribute f = V $ V.generate (reflectDim (Proxy :: Proxy n)) $ \i -> fmap (\(V v) -> V.unsafeIndex v i) f + {-# INLINE distribute #-} + +instance Hashable a => Hashable (V n a) where + hashWithSalt s0 (V v) = + V.foldl' (\s a -> s `hashWithSalt` a) s0 v + `hashWithSalt` V.length v + +instance Dim n => Hashable1 (V n) where + liftHashWithSalt h s0 (V v) = + V.foldl' (\s a -> h s a) s0 v + `hashWithSalt` V.length v + {-# INLINE liftHashWithSalt #-} + +instance (Dim n, Storable a) => Storable (V n a) where + sizeOf _ = reflectDim (Proxy :: Proxy n) * sizeOf (undefined:: a) + {-# INLINE sizeOf #-} + alignment _ = alignment (undefined :: a) + {-# INLINE alignment #-} + poke ptr (V xs) = Foldable.forM_ [0..reflectDim (Proxy :: Proxy n)-1] $ \i -> + pokeElemOff ptr' i (V.unsafeIndex xs i) + where ptr' = castPtr ptr + {-# INLINE poke #-} + peek ptr = V <$> V.generateM (reflectDim (Proxy :: Proxy n)) (peekElemOff ptr') + where ptr' = castPtr ptr + {-# INLINE peek #-} + +instance (Dim n, Epsilon a) => Epsilon (V n a) where + nearZero = nearZero . quadrance + {-# INLINE nearZero #-} + +instance Dim n => Metric (V n) where + dot (V a) (V b) = V.sum $ V.zipWith (*) a b + {-# INLINE dot #-} + +-- TODO: instance (Dim n, Ix a) => Ix (V n a) + +fromVector :: forall n a. Dim n => Vector a -> Maybe (V n a) +fromVector v + | V.length v == reflectDim (Proxy :: Proxy n) = Just (V v) + | otherwise = Nothing + +#if !(MIN_VERSION_reflection(1,3,0)) && defined(MIN_VERSION_template_haskell) +data Z -- 0 +data D (n :: *) -- 2n +data SD (n :: *) -- 2n+1 +data PD (n :: *) -- 2n-1 + +instance Reifies Z Int where + reflect _ = 0 + {-# INLINE reflect #-} + +retagD :: (Proxy n -> a) -> proxy (D n) -> a +retagD f _ = f Proxy +{-# INLINE retagD #-} + +retagSD :: (Proxy n -> a) -> proxy (SD n) -> a +retagSD f _ = f Proxy +{-# INLINE retagSD #-} + +retagPD :: (Proxy n -> a) -> proxy (PD n) -> a +retagPD f _ = f Proxy +{-# INLINE retagPD #-} + +instance Reifies n Int => Reifies (D n) Int where + reflect = (\n -> n+n) <$> retagD reflect + {-# INLINE reflect #-} + +instance Reifies n Int => Reifies (SD n) Int where + reflect = (\n -> n+n+1) <$> retagSD reflect + {-# INLINE reflect #-} + +instance Reifies n Int => Reifies (PD n) Int where + reflect = (\n -> n+n-1) <$> retagPD reflect + {-# INLINE reflect #-} + +-- | This can be used to generate a template haskell splice for a type level version of a given 'int'. +-- +-- This does not use GHC TypeLits, instead it generates a numeric type by hand similar to the ones used +-- in the \"Functional Pearl: Implicit Dimurations\" paper by Oleg Kiselyov and Chung-Chieh Shan. +int :: Int -> TypeQ +int n = case quotRem n 2 of + (0, 0) -> conT ''Z + (q,-1) -> conT ''PD `appT` int q + (q, 0) -> conT ''D `appT` int q + (q, 1) -> conT ''SD `appT` int q + _ -> error "ghc is bad at math" +#endif + +instance Dim n => Representable (V n) where + type Rep (V n) = Int + tabulate = V . V.generate (reflectDim (Proxy :: Proxy n)) + {-# INLINE tabulate #-} + index (V xs) i = xs V.! i + {-# INLINE index #-} + +type instance Index (V n a) = Int +type instance IxValue (V n a) = a + +instance Ixed (V n a) where + ix i f v@(V as) + | i < 0 || i >= V.length as = pure v + | otherwise = vLens i f v + {-# INLINE ix #-} + +instance Dim n => MonadZip (V n) where + mzip (V as) (V bs) = V $ V.zip as bs + mzipWith f (V as) (V bs) = V $ V.zipWith f as bs + +instance Dim n => MonadFix (V n) where + mfix f = tabulate $ \r -> let a = Rep.index (f a) r in a + +instance Each (V n a) (V n b) a b where + each = traverse + {-# INLINE each #-} + +instance (Bounded a, Dim n) => Bounded (V n a) where + minBound = pure minBound + {-# INLINE minBound #-} + maxBound = pure maxBound + {-# INLINE maxBound #-} + +vConstr :: Constr +vConstr = mkConstr vDataType "variadic" [] Prefix +{-# NOINLINE vConstr #-} + +vDataType :: DataType +vDataType = mkDataType "Linear.V.V" [vConstr] +{-# NOINLINE vDataType #-} + +instance (Typeable (V n), Typeable (V n a), Dim n, Data a) => Data (V n a) where + gfoldl f z (V as) = z (V . V.fromList) `f` V.toList as + toConstr _ = vConstr + gunfold k z c = case constrIndex c of + 1 -> k (z (V . V.fromList)) + _ -> error "gunfold" + dataTypeOf _ = vDataType + dataCast1 f = gcast1 f + +instance Dim n => Serial1 (V n) where + serializeWith = traverse_ + deserializeWith f = sequenceA $ pure f + +instance (Dim n, Serial a) => Serial (V n a) where + serialize = traverse_ serialize + deserialize = sequenceA $ pure deserialize + +instance (Dim n, Binary a) => Binary (V n a) where + put = serializeWith Binary.put + get = deserializeWith Binary.get + +instance (Dim n, Serialize a) => Serialize (V n a) where + put = serializeWith Cereal.put + get = deserializeWith Cereal.get + +instance Eq1 (V n) where + liftEq f0 (V as0) (V bs0) = go f0 (V.toList as0) (V.toList bs0) where + go _ [] [] = True + go f (a:as) (b:bs) = f a b && go f as bs + go _ _ _ = False + +instance Ord1 (V n) where + liftCompare f0 (V as0) (V bs0) = go f0 (V.toList as0) (V.toList bs0) where + go f (a:as) (b:bs) = f a b `mappend` go f as bs + go _ [] [] = EQ + go _ _ [] = GT + go _ [] _ = LT + +instance Show1 (V n) where + liftShowsPrec _ g d (V as) = showParen (d > 10) $ showString "V " . g (V.toList as) + +instance Dim n => Read1 (V n) where + liftReadsPrec _ g d = readParen (d > 10) $ \r -> + [ (V (V.fromList as), r2) + | ("V",r1) <- lex r + , (as, r2) <- g r1 + , P.length as == reflectDim (Proxy :: Proxy n) + ] + +data instance U.Vector (V n a) = V_VN {-# UNPACK #-} !Int !(U.Vector a) +data instance U.MVector s (V n a) = MV_VN {-# UNPACK #-} !Int !(U.MVector s a) +instance (Dim n, U.Unbox a) => U.Unbox (V n a) + +instance (Dim n, U.Unbox a) => M.MVector U.MVector (V n a) where + {-# INLINE basicLength #-} + {-# INLINE basicUnsafeSlice #-} + {-# INLINE basicOverlaps #-} + {-# INLINE basicUnsafeNew #-} + {-# INLINE basicUnsafeRead #-} + {-# INLINE basicUnsafeWrite #-} + basicLength (MV_VN n _) = n + basicUnsafeSlice m n (MV_VN _ v) = MV_VN n (M.basicUnsafeSlice (d*m) (d*n) v) + where d = reflectDim (Proxy :: Proxy n) + basicOverlaps (MV_VN _ v) (MV_VN _ u) = M.basicOverlaps v u + basicUnsafeNew n = liftM (MV_VN n) (M.basicUnsafeNew (d*n)) + where d = reflectDim (Proxy :: Proxy n) + basicUnsafeRead (MV_VN _ v) i = + liftM V $ V.generateM d (\j -> M.basicUnsafeRead v (d*i+j)) + where d = reflectDim (Proxy :: Proxy n) + basicUnsafeWrite (MV_VN _ v0) i (V vn0) = let d0 = V.length vn0 in go v0 vn0 d0 (d0*i) 0 + where + go v vn d o j + | j >= d = return () + | otherwise = do + a <- liftBox $ G.basicUnsafeIndexM vn j + M.basicUnsafeWrite v o a + go v vn d (o+1) (j+1) + basicInitialize (MV_VN _ v) = M.basicInitialize v + {-# INLINE basicInitialize #-} + +liftBox :: Monad m => Box a -> m a +liftBox (Box a) = return a +{-# INLINE liftBox #-} + +instance (Dim n, U.Unbox a) => G.Vector U.Vector (V n a) where + {-# INLINE basicUnsafeFreeze #-} + {-# INLINE basicUnsafeThaw #-} + {-# INLINE basicLength #-} + {-# INLINE basicUnsafeSlice #-} + {-# INLINE basicUnsafeIndexM #-} + basicUnsafeFreeze (MV_VN n v) = liftM ( V_VN n) (G.basicUnsafeFreeze v) + basicUnsafeThaw ( V_VN n v) = liftM (MV_VN n) (G.basicUnsafeThaw v) + basicLength ( V_VN n _) = n + basicUnsafeSlice m n (V_VN _ v) = V_VN n (G.basicUnsafeSlice (d*m) (d*n) v) + where d = reflectDim (Proxy :: Proxy n) + basicUnsafeIndexM (V_VN _ v) i = + liftM V $ V.generateM d (\j -> G.basicUnsafeIndexM v (d*i+j)) + where d = reflectDim (Proxy :: Proxy n) + +vLens :: Int -> Lens' (V n a) a +vLens i = \f (V v) -> f (v V.! i) <&> \a -> V (v V.// [(i, a)]) +{-# INLINE vLens #-} + +instance ( 1 <= n) => Field1 (V n a) (V n a) a a where _1 = vLens 0 +instance ( 2 <= n) => Field2 (V n a) (V n a) a a where _2 = vLens 1 +instance ( 3 <= n) => Field3 (V n a) (V n a) a a where _3 = vLens 2 +instance ( 4 <= n) => Field4 (V n a) (V n a) a a where _4 = vLens 3 +instance ( 5 <= n) => Field5 (V n a) (V n a) a a where _5 = vLens 4 +instance ( 6 <= n) => Field6 (V n a) (V n a) a a where _6 = vLens 5 +instance ( 7 <= n) => Field7 (V n a) (V n a) a a where _7 = vLens 6 +instance ( 8 <= n) => Field8 (V n a) (V n a) a a where _8 = vLens 7 +instance ( 9 <= n) => Field9 (V n a) (V n a) a a where _9 = vLens 8 +instance (10 <= n) => Field10 (V n a) (V n a) a a where _10 = vLens 9 +instance (11 <= n) => Field11 (V n a) (V n a) a a where _11 = vLens 10 +instance (12 <= n) => Field12 (V n a) (V n a) a a where _12 = vLens 11 +instance (13 <= n) => Field13 (V n a) (V n a) a a where _13 = vLens 12 +instance (14 <= n) => Field14 (V n a) (V n a) a a where _14 = vLens 13 +instance (15 <= n) => Field15 (V n a) (V n a) a a where _15 = vLens 14 +instance (16 <= n) => Field16 (V n a) (V n a) a a where _16 = vLens 15 +instance (17 <= n) => Field17 (V n a) (V n a) a a where _17 = vLens 16 +instance (18 <= n) => Field18 (V n a) (V n a) a a where _18 = vLens 17 +instance (19 <= n) => Field19 (V n a) (V n a) a a where _19 = vLens 18 diff --git a/src/Linear/V0.hs b/src/Linear/V0.hs --- a/src/Linear/V0.hs +++ b/src/Linear/V0.hs @@ -1,10 +1,17 @@ +{-# LANGUAGE CPP #-} {-# LANGUAGE DeriveDataTypeable #-} {-# LANGUAGE TypeFamilies #-} {-# LANGUAGE ScopedTypeVariables #-} +{-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE MultiParamTypeClasses #-} +{-# LANGUAGE DeriveGeneric #-} +{-# LANGUAGE Trustworthy #-} +{-# LANGUAGE DataKinds #-} +{-# LANGUAGE DeriveLift #-} + ----------------------------------------------------------------------------- -- | --- Module : Linear.V0 --- Copyright : (C) 2012-2013 Edward Kmett, +-- Copyright : (C) 2012-2015 Edward Kmett -- License : BSD-style (see the file LICENSE) -- -- Maintainer : Edward Kmett @@ -18,22 +25,50 @@ ) where import Control.Applicative +import Control.DeepSeq (NFData(rnf)) +import Control.Lens as Lens +import Control.Monad.Fix +import Control.Monad.Zip +import Data.Binary -- binary +import Data.Bytes.Serial -- bytes import Data.Data import Data.Distributive import Data.Foldable +import qualified Data.Foldable.WithIndex as WithIndex +import Data.Functor.Bind +import Data.Functor.Classes +import Data.Functor.Rep +import qualified Data.Functor.WithIndex as WithIndex +import Data.Hashable +import Data.Hashable.Lifted import Data.Ix -import Data.Traversable +#if !(MIN_VERSION_base(4,11,0)) import Data.Semigroup -import Data.Functor.Bind +#endif +import Data.Serialize -- cereal +import qualified Data.Traversable.WithIndex as WithIndex +import qualified Data.Vector as V import Foreign.Storable (Storable(..)) -import Linear.Core +import GHC.Generics (Generic, Generic1) +#if defined(MIN_VERSION_template_haskell) +import Language.Haskell.TH.Syntax (Lift) +#endif +import qualified Data.Vector.Generic.Mutable as M +import qualified Data.Vector.Generic as G +import qualified Data.Vector.Unboxed.Base as U import Linear.Metric import Linear.Epsilon import Linear.Vector +import Linear.V +import System.Random (Random(..), Uniform) +import System.Random.Stateful (UniformRange(..)) import Prelude hiding (sum) -- $setup +-- >>> import Control.Applicative -- >>> import Control.Lens +-- >>> import qualified Data.Foldable as F +-- >>> let sum xs = F.sum xs -- | A 0-dimensional vector -- @@ -43,8 +78,45 @@ -- >>> V0 + V0 -- V0 -- -data V0 a = V0 deriving (Eq,Ord,Show,Read,Ix,Enum,Data,Typeable) +data V0 a = V0 deriving (Eq,Ord,Show,Read,Ix,Enum,Data + ,Generic,Generic1 +#if defined(MIN_VERSION_template_haskell) + ,Lift +#endif + ) +instance Finite V0 where + type Size V0 = 0 + toV _ = V V.empty + fromV _ = V0 + +instance Random (V0 a) where + random g = (V0, g) + randomR _ g = (V0, g) + randomRs _ _ = repeat V0 + randoms _ = repeat V0 + +instance Uniform (V0 a) where + +instance UniformRange (V0 a) where + uniformRM (_, _) _ = pure V0 + +instance Serial1 V0 where + serializeWith _ = serialize + deserializeWith _ = deserialize + +instance Serial (V0 a) where + serialize V0 = return () + deserialize = return V0 + +instance Binary (V0 a) where + put V0 = return () + get = return V0 + +instance Serialize (V0 a) where + put V0 = return () + get = return V0 + instance Functor V0 where fmap _ V0 = V0 {-# INLINE fmap #-} @@ -54,6 +126,8 @@ instance Foldable V0 where foldMap _ V0 = mempty {-# INLINE foldMap #-} + null _ = True + length _ = 0 instance Traversable V0 where traverse _ V0 = pure V0 @@ -61,23 +135,40 @@ instance Apply V0 where V0 <.> V0 = V0 - {-@ INLINE (<.>) #-} + {-# INLINE (<.>) #-} instance Applicative V0 where pure _ = V0 {-# INLINE pure #-} V0 <*> V0 = V0 - {-@ INLINE (<*>) #-} + {-# INLINE (<*>) #-} -instance Additive V0 +instance Semigroup (V0 a) where + _ <> _ = V0 +instance Monoid (V0 a) where + mempty = V0 +#if !(MIN_VERSION_base(4,11,0)) + mappend _ _ = V0 +#endif + +instance Additive V0 where + zero = V0 + {-# INLINE zero #-} + liftU2 _ V0 V0 = V0 + {-# INLINE liftU2 #-} + liftI2 _ V0 V0 = V0 + {-# INLINE liftI2 #-} + instance Bind V0 where V0 >>- _ = V0 {-# INLINE (>>-) #-} instance Monad V0 where +#if !(MIN_VERSION_base(4,11,0)) return _ = V0 {-# INLINE return #-} +#endif V0 >>= _ = V0 {-# INLINE (>>=) #-} @@ -105,23 +196,67 @@ fromRational _ = V0 {-# INLINE fromRational #-} +instance Floating (V0 a) where + pi = V0 + {-# INLINE pi #-} + exp V0 = V0 + {-# INLINE exp #-} + sqrt V0 = V0 + {-# INLINE sqrt #-} + log V0 = V0 + {-# INLINE log #-} + V0 ** V0 = V0 + {-# INLINE (**) #-} + logBase V0 V0 = V0 + {-# INLINE logBase #-} + sin V0 = V0 + {-# INLINE sin #-} + tan V0 = V0 + {-# INLINE tan #-} + cos V0 = V0 + {-# INLINE cos #-} + asin V0 = V0 + {-# INLINE asin #-} + atan V0 = V0 + {-# INLINE atan #-} + acos V0 = V0 + {-# INLINE acos #-} + sinh V0 = V0 + {-# INLINE sinh #-} + tanh V0 = V0 + {-# INLINE tanh #-} + cosh V0 = V0 + {-# INLINE cosh #-} + asinh V0 = V0 + {-# INLINE asinh #-} + atanh V0 = V0 + {-# INLINE atanh #-} + acosh V0 = V0 + {-# INLINE acosh #-} + instance Metric V0 where dot V0 V0 = 0 {-# INLINE dot #-} -instance Core V0 where - core _ = V0 - {-# INLINE core #-} - instance Distributive V0 where distribute _ = V0 {-# INLINE distribute #-} -instance Epsilon a => Epsilon (V0 a) where +instance Hashable (V0 a) where + hash V0 = 0 + {-# INLINE hash #-} + hashWithSalt s V0 = s + {-# INLINE hashWithSalt #-} + +instance Hashable1 V0 where + liftHashWithSalt _ s V0 = s + {-# INLINE liftHashWithSalt #-} + +instance Epsilon (V0 a) where nearZero _ = True {-# INLINE nearZero #-} -instance Storable a => Storable (V0 a) where +instance Storable (V0 a) where sizeOf _ = 0 {-# INLINE sizeOf #-} alignment _ = 1 @@ -130,3 +265,97 @@ {-# INLINE poke #-} peek _ = return V0 {-# INLINE peek #-} + +instance WithIndex.FunctorWithIndex (E V0) V0 where + imap _ V0 = V0 + {-# INLINE imap #-} + +instance WithIndex.FoldableWithIndex (E V0) V0 where + ifoldMap _ V0 = mempty + {-# INLINE ifoldMap #-} + +instance WithIndex.TraversableWithIndex (E V0) V0 where + itraverse _ V0 = pure V0 + {-# INLINE itraverse #-} + +#if !MIN_VERSION_lens(5,0,0) +instance Lens.FunctorWithIndex (E V0) V0 where imap = WithIndex.imap +instance Lens.FoldableWithIndex (E V0) V0 where ifoldMap = WithIndex.ifoldMap +instance Lens.TraversableWithIndex (E V0) V0 where itraverse = WithIndex.itraverse +#endif + +instance Representable V0 where + type Rep V0 = E V0 + tabulate _ = V0 + {-# INLINE tabulate #-} + index xs (E l) = view l xs + {-# INLINE index #-} + +type instance Index (V0 a) = E V0 +type instance IxValue (V0 a) = a + +instance Ixed (V0 a) where + ix i = el i + {-# INLINE ix #-} + +instance Each (V0 a) (V0 b) a b where + each = traverse + {-# INLINE each #-} + +newtype instance U.Vector (V0 a) = V_V0 Int +newtype instance U.MVector s (V0 a) = MV_V0 Int +instance U.Unbox (V0 a) + +instance M.MVector U.MVector (V0 a) where + {-# INLINE basicLength #-} + {-# INLINE basicUnsafeSlice #-} + {-# INLINE basicOverlaps #-} + {-# INLINE basicUnsafeNew #-} + {-# INLINE basicUnsafeRead #-} + {-# INLINE basicUnsafeWrite #-} + basicLength (MV_V0 n) = n + basicUnsafeSlice _ n _ = MV_V0 n + basicOverlaps _ _ = False + basicUnsafeNew n = return (MV_V0 n) + basicUnsafeRead _ _ = return V0 + basicUnsafeWrite _ _ _ = return () + basicInitialize _ = return () + {-# INLINE basicInitialize #-} + +instance G.Vector U.Vector (V0 a) where + {-# INLINE basicUnsafeFreeze #-} + {-# INLINE basicUnsafeThaw #-} + {-# INLINE basicLength #-} + {-# INLINE basicUnsafeSlice #-} + {-# INLINE basicUnsafeIndexM #-} + basicUnsafeFreeze (MV_V0 n) = return (V_V0 n) + basicUnsafeThaw (V_V0 n) = return (MV_V0 n) + basicLength (V_V0 n) = n + basicUnsafeSlice _ n _ = V_V0 n + basicUnsafeIndexM _ _ = return V0 + +instance MonadZip V0 where + mzip V0 V0 = V0 + mzipWith _ V0 V0 = V0 + munzip V0 = (V0, V0) + +instance MonadFix V0 where + mfix _ = V0 + +instance Bounded (V0 a) where + minBound = V0 + {-# INLINE minBound #-} + maxBound = V0 + {-# INLINE maxBound #-} + +instance NFData (V0 a) where + rnf V0 = () + +instance Eq1 V0 where + liftEq _ _ _ = True +instance Ord1 V0 where + liftCompare _ _ _ = EQ +instance Show1 V0 where + liftShowsPrec _ _ = showsPrec +instance Read1 V0 where + liftReadsPrec _ _ = readsPrec diff --git a/src/Linear/V1.hs b/src/Linear/V1.hs new file mode 100644 --- /dev/null +++ b/src/Linear/V1.hs @@ -0,0 +1,400 @@ +{-# LANGUAGE CPP #-} +{-# LANGUAGE DeriveDataTypeable #-} +{-# LANGUAGE DeriveFunctor #-} +{-# LANGUAGE DeriveFoldable #-} +{-# LANGUAGE DeriveTraversable #-} +{-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE MultiParamTypeClasses #-} +{-# LANGUAGE GeneralizedNewtypeDeriving #-} +{-# LANGUAGE TypeFamilies #-} +{-# LANGUAGE ScopedTypeVariables #-} +{-# LANGUAGE Trustworthy #-} +{-# LANGUAGE DeriveGeneric #-} +{-# LANGUAGE DataKinds #-} +{-# LANGUAGE DeriveLift #-} + +----------------------------------------------------------------------------- +-- | +-- Copyright : (C) 2012-2015 Edward Kmett +-- License : BSD-style (see the file LICENSE) +-- +-- Maintainer : Edward Kmett +-- Stability : experimental +-- Portability : non-portable +-- +-- 1-D Vectors +---------------------------------------------------------------------------- +module Linear.V1 + ( V1(..) + , R1(..) + , ex + ) where + +import Control.Applicative +import Control.DeepSeq (NFData) +import Control.Monad (liftM) +import Control.Monad.Fix +import Control.Monad.Zip +import Control.Lens as Lens +import Data.Binary as Binary +import Data.Bytes.Serial +import Data.Serialize as Cereal +import Data.Data +import Data.Distributive +import Data.Foldable +import qualified Data.Foldable.WithIndex as WithIndex +import Data.Functor.Bind +import Data.Functor.Classes +import Data.Functor.Rep +import qualified Data.Functor.WithIndex as WithIndex +import Data.Hashable +import Data.Hashable.Lifted +import Data.Semigroup.Foldable +import qualified Data.Traversable.WithIndex as WithIndex +import qualified Data.Vector as V +import Linear.V +import Foreign.Storable (Storable) +import GHC.Arr (Ix(..)) +import GHC.Generics (Generic, Generic1) +#if defined(MIN_VERSION_template_haskell) +import Language.Haskell.TH.Syntax (Lift) +#endif +import Linear.Metric +import Linear.Epsilon +import Linear.Vector +import Prelude hiding (sum) +import System.Random (Random(..), Uniform) +import System.Random.Stateful (UniformRange(..)) +#if !(MIN_VERSION_base(4,11,0)) +import Data.Semigroup +#endif + +import qualified Data.Vector.Generic.Mutable as M +import qualified Data.Vector.Generic as G +import qualified Data.Vector.Unboxed.Base as U + +-- $setup +-- >>> import Control.Applicative +-- >>> import Control.Lens +-- >>> import qualified Data.Foldable as F +-- >>> let sum xs = F.sum xs + +-- | A 1-dimensional vector +-- +-- >>> pure 1 :: V1 Int +-- V1 1 +-- +-- >>> V1 2 + V1 3 +-- V1 5 +-- +-- >>> V1 2 * V1 3 +-- V1 6 +-- +-- >>> sum (V1 2) +-- 2 + +--data V2 a = V2 !a !a deriving (Eq,Ord,Show,Read,Data) +newtype V1 a = V1 a + deriving (Eq,Ord,Show,Read,Data, + Functor,Traversable, + Epsilon,Storable,NFData + ,Generic,Generic1 +#if defined(MIN_VERSION_template_haskell) + ,Lift +#endif + ) + +instance Foldable V1 where + foldMap f (V1 a) = f a +#if MIN_VERSION_base(4,13,0) + foldMap' f (V1 a) = f a +#endif + null _ = False + length _ = 1 + +instance Finite V1 where + type Size V1 = 1 + toV (V1 a) = V (V.singleton a) + fromV (V v) = V1 (v V.! 0) + +instance Foldable1 V1 where + foldMap1 f (V1 a) = f a + {-# INLINE foldMap1 #-} + +instance Traversable1 V1 where + traverse1 f (V1 a) = V1 <$> f a + {-# INLINE traverse1 #-} + +instance Apply V1 where + V1 f <.> V1 x = V1 (f x) + {-# INLINE (<.>) #-} + +instance Applicative V1 where + pure = V1 + {-# INLINE pure #-} + V1 f <*> V1 x = V1 (f x) + {-# INLINE (<*>) #-} + +instance Additive V1 where + zero = pure 0 + {-# INLINE zero #-} + liftU2 = liftA2 + {-# INLINE liftU2 #-} + liftI2 = liftA2 + {-# INLINE liftI2 #-} + +instance Bind V1 where + V1 a >>- f = f a + {-# INLINE (>>-) #-} + +instance Monad V1 where +#if !(MIN_VERSION_base(4,11,0)) + return = V1 + {-# INLINE return #-} +#endif + V1 a >>= f = f a + {-# INLINE (>>=) #-} + +instance Num a => Num (V1 a) where + (+) = liftA2 (+) + {-# INLINE (+) #-} + (-) = liftA2 (-) + {-# INLINE (-) #-} + (*) = liftA2 (*) + {-# INLINE (*) #-} + negate = fmap negate + {-# INLINE negate #-} + abs = fmap abs + {-# INLINE abs #-} + signum = fmap signum + {-# INLINE signum #-} + fromInteger = pure . fromInteger + {-# INLINE fromInteger #-} + +instance Fractional a => Fractional (V1 a) where + recip = fmap recip + {-# INLINE recip #-} + (/) = liftA2 (/) + {-# INLINE (/) #-} + fromRational = pure . fromRational + {-# INLINE fromRational #-} + +instance Floating a => Floating (V1 a) where + pi = pure pi + {-# INLINE pi #-} + exp = fmap exp + {-# INLINE exp #-} + sqrt = fmap sqrt + {-# INLINE sqrt #-} + log = fmap log + {-# INLINE log #-} + (**) = liftA2 (**) + {-# INLINE (**) #-} + logBase = liftA2 logBase + {-# INLINE logBase #-} + sin = fmap sin + {-# INLINE sin #-} + tan = fmap tan + {-# INLINE tan #-} + cos = fmap cos + {-# INLINE cos #-} + asin = fmap asin + {-# INLINE asin #-} + atan = fmap atan + {-# INLINE atan #-} + acos = fmap acos + {-# INLINE acos #-} + sinh = fmap sinh + {-# INLINE sinh #-} + tanh = fmap tanh + {-# INLINE tanh #-} + cosh = fmap cosh + {-# INLINE cosh #-} + asinh = fmap asinh + {-# INLINE asinh #-} + atanh = fmap atanh + {-# INLINE atanh #-} + acosh = fmap acosh + {-# INLINE acosh #-} + +instance Hashable a => Hashable (V1 a) where + hash (V1 a) = hash a + hashWithSalt s (V1 a) = s `hashWithSalt` a + +instance Hashable1 V1 where + liftHashWithSalt h s (V1 a) = h s a + {-# INLINE liftHashWithSalt #-} + +instance Metric V1 where + dot (V1 a) (V1 b) = a * b + {-# INLINE dot #-} + +-- | A space that has at least 1 basis vector '_x'. +class R1 t where + -- | + -- >>> V1 2 ^._x + -- 2 + -- + -- >>> V1 2 & _x .~ 3 + -- V1 3 + -- + _x :: Lens' (t a) a + +ex :: R1 t => E t +ex = E _x + +instance R1 V1 where + _x f (V1 a) = V1 <$> f a + {-# INLINE _x #-} + +instance R1 Identity where + _x f (Identity a) = Identity <$> f a + {-# INLINE _x #-} + +instance Distributive V1 where + distribute f = V1 (fmap (\(V1 x) -> x) f) + {-# INLINE distribute #-} + +instance Ix a => Ix (V1 a) where + {-# SPECIALISE instance Ix (V1 Int) #-} + + range (V1 l1, V1 u1) = + [ V1 i1 | i1 <- range (l1,u1) ] + {-# INLINE range #-} + + unsafeIndex (V1 l1,V1 u1) (V1 i1) = unsafeIndex (l1,u1) i1 + {-# INLINE unsafeIndex #-} + + inRange (V1 l1,V1 u1) (V1 i1) = inRange (l1,u1) i1 + {-# INLINE inRange #-} + +instance Representable V1 where + type Rep V1 = E V1 + tabulate f = V1 (f ex) + {-# INLINE tabulate #-} + index xs (E l) = view l xs + {-# INLINE index #-} + +instance WithIndex.FunctorWithIndex (E V1) V1 where + imap f (V1 a) = V1 (f ex a) + {-# INLINE imap #-} + +instance WithIndex.FoldableWithIndex (E V1) V1 where + ifoldMap f (V1 a) = f ex a + {-# INLINE ifoldMap #-} + +instance WithIndex.TraversableWithIndex (E V1) V1 where + itraverse f (V1 a) = V1 <$> f ex a + {-# INLINE itraverse #-} + +#if !MIN_VERSION_lens(5,0,0) +instance Lens.FunctorWithIndex (E V1) V1 where imap = WithIndex.imap +instance Lens.FoldableWithIndex (E V1) V1 where ifoldMap = WithIndex.ifoldMap +instance Lens.TraversableWithIndex (E V1) V1 where itraverse = WithIndex.itraverse +#endif + +type instance Index (V1 a) = E V1 +type instance IxValue (V1 a) = a + +instance Ixed (V1 a) where + ix i = el i + {-# INLINE ix #-} + +instance Each (V1 a) (V1 b) a b where + each f (V1 x) = V1 <$> f x + {-# INLINE each #-} + +newtype instance U.Vector (V1 a) = V_V1 (U.Vector a) +newtype instance U.MVector s (V1 a) = MV_V1 (U.MVector s a) +instance U.Unbox a => U.Unbox (V1 a) + +instance U.Unbox a => M.MVector U.MVector (V1 a) where + {-# INLINE basicLength #-} + {-# INLINE basicUnsafeSlice #-} + {-# INLINE basicOverlaps #-} + {-# INLINE basicUnsafeNew #-} + {-# INLINE basicUnsafeRead #-} + {-# INLINE basicUnsafeWrite #-} + basicLength (MV_V1 v) = M.basicLength v + basicUnsafeSlice m n (MV_V1 v) = MV_V1 (M.basicUnsafeSlice m n v) + basicOverlaps (MV_V1 v) (MV_V1 u) = M.basicOverlaps v u + basicUnsafeNew n = liftM MV_V1 (M.basicUnsafeNew n) + basicUnsafeRead (MV_V1 v) i = liftM V1 (M.basicUnsafeRead v i) + basicUnsafeWrite (MV_V1 v) i (V1 x) = M.basicUnsafeWrite v i x + basicInitialize (MV_V1 v) = M.basicInitialize v + {-# INLINE basicInitialize #-} + +instance U.Unbox a => G.Vector U.Vector (V1 a) where + {-# INLINE basicUnsafeFreeze #-} + {-# INLINE basicUnsafeThaw #-} + {-# INLINE basicLength #-} + {-# INLINE basicUnsafeSlice #-} + {-# INLINE basicUnsafeIndexM #-} + basicUnsafeFreeze (MV_V1 v) = liftM V_V1 (G.basicUnsafeFreeze v) + basicUnsafeThaw (V_V1 v) = liftM MV_V1 (G.basicUnsafeThaw v) + basicLength (V_V1 v) = G.basicLength v + basicUnsafeSlice m n (V_V1 v) = V_V1 (G.basicUnsafeSlice m n v) + basicUnsafeIndexM (V_V1 v) i = liftM V1 (G.basicUnsafeIndexM v i) + +instance MonadZip V1 where + mzip (V1 a) (V1 b) = V1 (a, b) + mzipWith f (V1 a) (V1 b) = V1 (f a b) + munzip (V1 (a,b)) = (V1 a, V1 b) + +instance MonadFix V1 where + mfix f = V1 (let V1 a = f a in a) + +instance Bounded a => Bounded (V1 a) where + minBound = pure minBound + {-# INLINE minBound #-} + maxBound = pure maxBound + {-# INLINE maxBound #-} + +instance Serial1 V1 where + serializeWith f (V1 a) = f a + deserializeWith m = V1 `liftM` m + +instance Serial a => Serial (V1 a) where + serialize (V1 a) = serialize a + deserialize = V1 `liftM` deserialize + +instance Binary a => Binary (V1 a) where + put = serializeWith Binary.put + get = deserializeWith Binary.get + +instance Serialize a => Serialize (V1 a) where + put = serializeWith Cereal.put + get = deserializeWith Cereal.get + +instance Random a => Random (V1 a) where + random g = case random g of (a, g') -> (V1 a, g') + randoms g = V1 <$> randoms g + randomR (V1 a, V1 b) g = case randomR (a, b) g of (a', g') -> (V1 a', g') + randomRs (V1 a, V1 b) g = V1 <$> randomRs (a, b) g + +instance Uniform a => Uniform (V1 a) where + +instance UniformRange a => UniformRange (V1 a) where + uniformRM (V1 a, V1 b) g = V1 <$> uniformRM (a, b) g + +instance Eq1 V1 where + liftEq f (V1 a) (V1 b) = f a b +instance Ord1 V1 where + liftCompare f (V1 a) (V1 b) = f a b +instance Show1 V1 where + liftShowsPrec f _ d (V1 a) = showParen (d >= 10) $ showString "V1 " . f d a +instance Read1 V1 where + liftReadsPrec f _ = readsData $ readsUnaryWith f "V1" V1 + +instance Field1 (V1 a) (V1 b) a b where + _1 f (V1 x) = V1 <$> f x + +instance Semigroup a => Semigroup (V1 a) where + (<>) = liftA2 (<>) + +instance Monoid a => Monoid (V1 a) where + mempty = pure mempty +#if !(MIN_VERSION_base(4,11,0)) + mappend = liftA2 mappend +#endif + diff --git a/src/Linear/V2.hs b/src/Linear/V2.hs --- a/src/Linear/V2.hs +++ b/src/Linear/V2.hs @@ -1,11 +1,18 @@ {-# LANGUAGE DeriveDataTypeable #-} {-# LANGUAGE TypeFamilies #-} {-# LANGUAGE ScopedTypeVariables #-} --- {-# OPTIONS_GHC -fno-warn-name-shadowing #-} +{-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE RankNTypes #-} +{-# LANGUAGE MultiParamTypeClasses #-} +{-# LANGUAGE CPP #-} +{-# LANGUAGE Trustworthy #-} +{-# LANGUAGE DeriveGeneric #-} +{-# LANGUAGE DataKinds #-} +{-# LANGUAGE DeriveLift #-} + ----------------------------------------------------------------------------- -- | --- Module : Linear.V2 --- Copyright : (C) 2012-2013 Edward Kmett, +-- Copyright : (C) 2012-2015 Edward Kmett -- License : BSD-style (see the file LICENSE) -- -- Maintainer : Edward Kmett @@ -16,30 +23,63 @@ ---------------------------------------------------------------------------- module Linear.V2 ( V2(..) + , R1(..) , R2(..) + , _yx + , ex, ey , perp + , angle + , unangle + , crossZ ) where import Control.Applicative +import Control.DeepSeq (NFData(rnf)) +import Control.Monad (liftM) +import Control.Monad.Fix +import Control.Monad.Zip +import Control.Lens as Lens hiding ((<.>)) +import Data.Binary as Binary +import Data.Bytes.Serial import Data.Data import Data.Distributive import Data.Foldable -import Data.Traversable +import qualified Data.Foldable.WithIndex as WithIndex +import Data.Functor.Bind +import Data.Functor.Classes +import Data.Functor.Rep +import qualified Data.Functor.WithIndex as WithIndex +import Data.Hashable +import Data.Hashable.Lifted import Data.Semigroup import Data.Semigroup.Foldable -import Data.Semigroup.Traversable -import Data.Functor.Bind +import Data.Serialize as Cereal +import qualified Data.Traversable.WithIndex as WithIndex +import qualified Data.Vector as V import Foreign.Ptr (castPtr) import Foreign.Storable (Storable(..)) import GHC.Arr (Ix(..)) -import Linear.Core +import GHC.Generics (Generic, Generic1) +#if defined(MIN_VERSION_template_haskell) +import Language.Haskell.TH.Syntax (Lift) +#endif +import qualified Data.Vector.Generic.Mutable as M +import qualified Data.Vector.Generic as G +import qualified Data.Vector.Unboxed.Base as U import Linear.Metric import Linear.Epsilon +import Linear.V import Linear.Vector +import Linear.V1 (R1(..),ex) import Prelude hiding (sum) +import System.Random (Random(..), Uniform) +import System.Random.Stateful (UniformRange(..)) -- $setup +-- >>> import Control.Applicative -- >>> import Control.Lens +-- >>> import qualified Data.Foldable as F +-- >>> let sum xs = F.sum xs -- | A 2-dimensional vector -- @@ -55,8 +95,34 @@ -- >>> sum (V2 1 2) -- 3 -data V2 a = V2 a a deriving (Eq,Ord,Show,Read,Data,Typeable) +data V2 a = V2 !a !a deriving + (Eq,Ord,Show,Read,Data + ,Generic,Generic1 +#if defined(MIN_VERSION_template_haskell) + ,Lift +#endif + ) +instance Finite V2 where + type Size V2 = 2 + toV (V2 a b) = V (V.fromListN 2 [a,b]) + fromV (V v) = V2 (v V.! 0) (v V.! 1) + +instance Random a => Random (V2 a) where + random g = case random g of + (a, g') -> case random g' of + (b, g'') -> (V2 a b, g'') + {-# inline random #-} + randomR (V2 a b, V2 c d) g = case randomR (a, c) g of + (x, g') -> case randomR (b, d) g' of + (y, g'') -> (V2 x y, g'') + {-# inline randomR #-} + +instance Uniform a => Uniform (V2 a) where + +instance UniformRange a => UniformRange (V2 a) where + uniformRM (V2 a b, V2 c d) g = V2 <$> uniformRM (a, c) g <*> uniformRM (b, d) g + instance Functor V2 where fmap f (V2 a b) = V2 (f a) (f b) {-# INLINE fmap #-} @@ -66,6 +132,12 @@ instance Foldable V2 where foldMap f (V2 a b) = f a `mappend` f b {-# INLINE foldMap #-} +#if MIN_VERSION_base(4,13,0) + foldMap' f (V2 a b) = f a `mappend` f b + {-# INLINE foldMap' #-} +#endif + null _ = False + length _ = 2 instance Traversable V2 where traverse f (V2 a b) = V2 <$> f a <*> f b @@ -81,16 +153,30 @@ instance Apply V2 where V2 a b <.> V2 d e = V2 (a d) (b e) - {-@ INLINE (<.>) #-} + {-# INLINE (<.>) #-} instance Applicative V2 where pure a = V2 a a {-# INLINE pure #-} V2 a b <*> V2 d e = V2 (a d) (b e) - {-@ INLINE (<*>) #-} + {-# INLINE (<*>) #-} -instance Additive V2 +instance Hashable a => Hashable (V2 a) where + hashWithSalt s (V2 a b) = s `hashWithSalt` a `hashWithSalt` b + {-# INLINE hashWithSalt #-} +instance Hashable1 V2 where + liftHashWithSalt h s (V2 a b) = s `h` a `h` b + {-# INLINE liftHashWithSalt #-} + +instance Additive V2 where + zero = pure 0 + {-# INLINE zero #-} + liftU2 = liftA2 + {-# INLINE liftU2 #-} + liftI2 = liftA2 + {-# INLINE liftI2 #-} + instance Bind V2 where V2 a b >>- f = V2 a' b' where V2 a' _ = f a @@ -98,8 +184,10 @@ {-# INLINE (>>-) #-} instance Monad V2 where +#if !(MIN_VERSION_base(4,11,0)) return a = V2 a a {-# INLINE return #-} +#endif V2 a b >>= f = V2 a' b' where V2 a' _ = f a V2 _ b' = f b @@ -129,26 +217,50 @@ fromRational = pure . fromRational {-# INLINE fromRational #-} +instance Floating a => Floating (V2 a) where + pi = pure pi + {-# INLINE pi #-} + exp = fmap exp + {-# INLINE exp #-} + sqrt = fmap sqrt + {-# INLINE sqrt #-} + log = fmap log + {-# INLINE log #-} + (**) = liftA2 (**) + {-# INLINE (**) #-} + logBase = liftA2 logBase + {-# INLINE logBase #-} + sin = fmap sin + {-# INLINE sin #-} + tan = fmap tan + {-# INLINE tan #-} + cos = fmap cos + {-# INLINE cos #-} + asin = fmap asin + {-# INLINE asin #-} + atan = fmap atan + {-# INLINE atan #-} + acos = fmap acos + {-# INLINE acos #-} + sinh = fmap sinh + {-# INLINE sinh #-} + tanh = fmap tanh + {-# INLINE tanh #-} + cosh = fmap cosh + {-# INLINE cosh #-} + asinh = fmap asinh + {-# INLINE asinh #-} + atanh = fmap atanh + {-# INLINE atanh #-} + acosh = fmap acosh + {-# INLINE acosh #-} + instance Metric V2 where dot (V2 a b) (V2 c d) = a * c + b * d {-# INLINE dot #-} -- | A space that distinguishes 2 orthogonal basis vectors '_x' and '_y', but may have more. -class R2 t where - -- | - -- >>> V2 1 2 ^._x - -- 1 - -- - -- >>> V2 1 2 & _x .~ 3 - -- V2 3 2 - -- - -- @ - -- '_x' :: Lens' (t a) a - -- @ - _x :: Functor f => (a -> f a) -> t a -> f (t a) - _x = _xy._x - {-# INLINE _x #-} - +class R1 t => R2 t where -- | -- >>> V2 1 2 ^._y -- 2 @@ -156,31 +268,32 @@ -- >>> V2 1 2 & _y .~ 3 -- V2 1 3 -- - -- @ - -- '_y' :: Lens' (t a) a - -- @ - _y :: Functor f => (a -> f a) -> t a -> f (t a) + _y :: Lens' (t a) a _y = _xy._y {-# INLINE _y #-} - -- | - -- @ - -- '_xy' :: Lens' (t a) ('V2' a) - -- @ - _xy :: Functor f => (V2 a -> f (V2 a)) -> t a -> f (t a) + _xy :: Lens' (t a) (V2 a) -instance R2 V2 where +-- | +-- >>> V2 1 2 ^. _yx +-- V2 2 1 +_yx :: R2 t => Lens' (t a) (V2 a) +_yx f = _xy $ \(V2 a b) -> f (V2 b a) <&> \(V2 b' a') -> V2 a' b' +{-# INLINE _yx #-} + +ey :: R2 t => E t +ey = E _y + +instance R1 V2 where _x f (V2 a b) = (`V2` b) <$> f a {-# INLINE _x #-} + +instance R2 V2 where _y f (V2 a b) = V2 a <$> f b {-# INLINE _y #-} _xy = id {-# INLINE _xy #-} -instance Core V2 where - core f = V2 (f _x) (f _y) - {-# INLINE core #-} - instance Distributive V2 where distribute f = V2 (fmap (\(V2 x _) -> x) f) (fmap (\(V2 _ y) -> y) f) {-# INLINE distribute #-} @@ -223,3 +336,156 @@ inRange (V2 l1 l2,V2 u1 u2) (V2 i1 i2) = inRange (l1,u1) i1 && inRange (l2,u2) i2 {-# INLINE inRange #-} + +instance Representable V2 where + type Rep V2 = E V2 + tabulate f = V2 (f ex) (f ey) + {-# INLINE tabulate #-} + index xs (E l) = view l xs + {-# INLINE index #-} + +instance WithIndex.FunctorWithIndex (E V2) V2 where + imap f (V2 a b) = V2 (f ex a) (f ey b) + {-# INLINE imap #-} + +instance WithIndex.FoldableWithIndex (E V2) V2 where + ifoldMap f (V2 a b) = f ex a `mappend` f ey b + {-# INLINE ifoldMap #-} + +instance WithIndex.TraversableWithIndex (E V2) V2 where + itraverse f (V2 a b) = V2 <$> f ex a <*> f ey b + {-# INLINE itraverse #-} + +#if !MIN_VERSION_lens(5,0,0) +instance Lens.FunctorWithIndex (E V2) V2 where imap = WithIndex.imap +instance Lens.FoldableWithIndex (E V2) V2 where ifoldMap = WithIndex.ifoldMap +instance Lens.TraversableWithIndex (E V2) V2 where itraverse = WithIndex.itraverse +#endif + +type instance Index (V2 a) = E V2 +type instance IxValue (V2 a) = a + +instance Ixed (V2 a) where + ix i = el i + {-# INLINE ix #-} + +instance Each (V2 a) (V2 b) a b where + each = traverse + {-# INLINE each #-} + +data instance U.Vector (V2 a) = V_V2 {-# UNPACK #-} !Int !(U.Vector a) +data instance U.MVector s (V2 a) = MV_V2 {-# UNPACK #-} !Int !(U.MVector s a) +instance U.Unbox a => U.Unbox (V2 a) + +instance U.Unbox a => M.MVector U.MVector (V2 a) where + {-# INLINE basicLength #-} + {-# INLINE basicUnsafeSlice #-} + {-# INLINE basicOverlaps #-} + {-# INLINE basicUnsafeNew #-} + {-# INLINE basicUnsafeRead #-} + {-# INLINE basicUnsafeWrite #-} + basicLength (MV_V2 n _) = n + basicUnsafeSlice m n (MV_V2 _ v) = MV_V2 n (M.basicUnsafeSlice (2*m) (2*n) v) + basicOverlaps (MV_V2 _ v) (MV_V2 _ u) = M.basicOverlaps v u + basicUnsafeNew n = liftM (MV_V2 n) (M.basicUnsafeNew (2*n)) + basicUnsafeRead (MV_V2 _ v) i = + do let o = 2*i + x <- M.basicUnsafeRead v o + y <- M.basicUnsafeRead v (o+1) + return (V2 x y) + basicUnsafeWrite (MV_V2 _ v) i (V2 x y) = + do let o = 2*i + M.basicUnsafeWrite v o x + M.basicUnsafeWrite v (o+1) y + basicInitialize (MV_V2 _ v) = M.basicInitialize v + {-# INLINE basicInitialize #-} + +instance U.Unbox a => G.Vector U.Vector (V2 a) where + {-# INLINE basicUnsafeFreeze #-} + {-# INLINE basicUnsafeThaw #-} + {-# INLINE basicLength #-} + {-# INLINE basicUnsafeSlice #-} + {-# INLINE basicUnsafeIndexM #-} + basicUnsafeFreeze (MV_V2 n v) = liftM ( V_V2 n) (G.basicUnsafeFreeze v) + basicUnsafeThaw ( V_V2 n v) = liftM (MV_V2 n) (G.basicUnsafeThaw v) + basicLength ( V_V2 n _) = n + basicUnsafeSlice m n (V_V2 _ v) = V_V2 n (G.basicUnsafeSlice (2*m) (2*n) v) + basicUnsafeIndexM (V_V2 _ v) i = + do let o = 2*i + x <- G.basicUnsafeIndexM v o + y <- G.basicUnsafeIndexM v (o+1) + return (V2 x y) + +instance MonadZip V2 where + mzipWith = liftA2 + +instance MonadFix V2 where + mfix f = V2 (let V2 a _ = f a in a) + (let V2 _ a = f a in a) + +angle :: Floating a => a -> V2 a +angle a = V2 (cos a) (sin a) + +unangle :: (Floating a, Ord a) => V2 a -> a +unangle a@(V2 ax ay) = + let alpha = asin $ ay / norm a + in if ax < 0 + then pi - alpha + else alpha + +-- | The Z-component of the cross product of two vectors in the XY-plane. +-- +-- >>> crossZ (V2 1 0) (V2 0 1) +-- 1 +crossZ :: Num a => V2 a -> V2 a -> a +crossZ (V2 x1 y1) (V2 x2 y2) = x1*y2 - y1*x2 +{-# INLINE crossZ #-} + +instance Bounded a => Bounded (V2 a) where + minBound = pure minBound + {-# INLINE minBound #-} + maxBound = pure maxBound + {-# INLINE maxBound #-} + +instance NFData a => NFData (V2 a) where + rnf (V2 a b) = rnf a `seq` rnf b + +instance Serial1 V2 where + serializeWith = traverse_ + deserializeWith k = V2 <$> k <*> k + +instance Serial a => Serial (V2 a) where + serialize = serializeWith serialize + deserialize = deserializeWith deserialize + +instance Binary a => Binary (V2 a) where + put = serializeWith Binary.put + get = deserializeWith Binary.get + +instance Serialize a => Serialize (V2 a) where + put = serializeWith Cereal.put + get = deserializeWith Cereal.get + +instance Eq1 V2 where + liftEq f (V2 a b) (V2 c d) = f a c && f b d +instance Ord1 V2 where + liftCompare f (V2 a b) (V2 c d) = f a c `mappend` f b d +instance Read1 V2 where + liftReadsPrec f _ = readsData $ readsBinaryWith f f "V2" V2 +instance Show1 V2 where + liftShowsPrec f _ d (V2 a b) = showsBinaryWith f f "V2" d a b + +instance Field1 (V2 a) (V2 a) a a where + _1 f (V2 x y) = f x <&> \x' -> V2 x' y + +instance Field2 (V2 a) (V2 a) a a where + _2 f (V2 x y) = f y <&> \y' -> V2 x y' + +instance Semigroup a => Semigroup (V2 a) where + (<>) = liftA2 (<>) + +instance Monoid a => Monoid (V2 a) where + mempty = pure mempty +#if !(MIN_VERSION_base(4,11,0)) + mappend = liftA2 mappend +#endif diff --git a/src/Linear/V3.hs b/src/Linear/V3.hs --- a/src/Linear/V3.hs +++ b/src/Linear/V3.hs @@ -1,8 +1,18 @@ -{-# LANGUAGE DeriveDataTypeable, ScopedTypeVariables #-} +{-# LANGUAGE DeriveDataTypeable #-} +{-# LANGUAGE ScopedTypeVariables #-} +{-# LANGUAGE TypeFamilies #-} +{-# LANGUAGE MultiParamTypeClasses #-} +{-# LANGUAGE RankNTypes #-} +{-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE CPP #-} +{-# LANGUAGE Trustworthy #-} +{-# LANGUAGE DeriveGeneric #-} +{-# LANGUAGE DataKinds #-} +{-# LANGUAGE DeriveLift #-} + ----------------------------------------------------------------------------- -- | --- Module : Linear.V3 --- Copyright : (C) 2012-2013 Edward Kmett, +-- Copyright : (C) 2012-2015 Edward Kmett -- License : BSD-style (see the file LICENSE) -- -- Maintainer : Edward Kmett @@ -14,33 +24,76 @@ module Linear.V3 ( V3(..) , cross, triple + , R1(..) , R2(..) + , _yx , R3(..) + , _xz, _yz, _zx, _zy + , _xzy, _yxz, _yzx, _zxy, _zyx + , ex, ey, ez ) where +#if !MIN_VERSION_base(4,18,0) import Control.Applicative +#endif +import Control.DeepSeq (NFData(rnf)) +import Control.Monad (liftM) +import Control.Monad.Fix +import Control.Monad.Zip +import Control.Lens as Lens hiding ((<.>)) +import Data.Binary as Binary -- binary +import Data.Bytes.Serial -- bytes import Data.Data import Data.Distributive import Data.Foldable +import qualified Data.Foldable.WithIndex as WithIndex import Data.Functor.Bind -import Data.Traversable +import Data.Functor.Classes +import Data.Functor.Rep +import qualified Data.Functor.WithIndex as WithIndex +import Data.Hashable +import Data.Hashable.Lifted +#if !(MIN_VERSION_base(4,11,0)) import Data.Semigroup +#endif import Data.Semigroup.Foldable -import Data.Semigroup.Traversable +import Data.Serialize as Cereal -- cereal +import qualified Data.Traversable.WithIndex as WithIndex +import qualified Data.Vector as V +import qualified Data.Vector.Generic.Mutable as M +import qualified Data.Vector.Generic as G +import qualified Data.Vector.Unboxed.Base as U import Foreign.Ptr (castPtr) import Foreign.Storable (Storable(..)) import GHC.Arr (Ix(..)) -import Linear.Core +import GHC.Generics (Generic, Generic1) +#if defined(MIN_VERSION_template_haskell) +import Language.Haskell.TH.Syntax (Lift) +#endif import Linear.Epsilon import Linear.Metric +import Linear.V import Linear.V2 import Linear.Vector +import System.Random (Random(..), Uniform) +import System.Random.Stateful (UniformRange(..)) -{-# ANN module "HLint: ignore Reduce duplication" #-} +-- $setup +-- >>> import Control.Lens hiding (index) -- | A 3-dimensional vector -data V3 a = V3 a a a deriving (Eq,Ord,Show,Read,Data,Typeable) +data V3 a = V3 !a !a !a deriving (Eq,Ord,Show,Read,Data + ,Generic,Generic1 +#if defined(MIN_VERSION_template_haskell) + ,Lift +#endif + ) +instance Finite V3 where + type Size V3 = 3 + toV (V3 a b c) = V (V.fromListN 3 [a,b,c]) + fromV (V v) = V3 (v V.! 0) (v V.! 1) (v V.! 2) + instance Functor V3 where fmap f (V3 a b c) = V3 (f a) (f b) (f c) {-# INLINE fmap #-} @@ -50,7 +103,31 @@ instance Foldable V3 where foldMap f (V3 a b c) = f a `mappend` f b `mappend` f c {-# INLINE foldMap #-} +#if MIN_VERSION_base(4,13,0) + foldMap' f (V3 a b c) = (f a `mappend` f b) `mappend` f c + {-# INLINE foldMap' #-} +#endif + null _ = False + length _ = 3 +instance Random a => Random (V3 a) where + random g = case random g of + (a, g') -> case random g' of + (b, g'') -> case random g'' of + (c, g''') -> (V3 a b c, g''') + randomR (V3 a b c, V3 a' b' c') g = case randomR (a,a') g of + (a'', g') -> case randomR (b,b') g' of + (b'', g'') -> case randomR (c,c') g'' of + (c'', g''') -> (V3 a'' b'' c'', g''') + +instance Uniform a => Uniform (V3 a) where + +instance UniformRange a => UniformRange (V3 a) where + uniformRM (V3 a b c, V3 a' b' c') g = V3 + <$> uniformRM (a, a') g + <*> uniformRM (b, b') g + <*> uniformRM (c, c') g + instance Traversable V3 where traverse f (V3 a b c) = V3 <$> f a <*> f b <*> f c {-# INLINE traverse #-} @@ -73,7 +150,13 @@ V3 a b c <*> V3 d e f = V3 (a d) (b e) (c f) {-# INLINE (<*>) #-} -instance Additive V3 +instance Additive V3 where + zero = pure 0 + {-# INLINE zero #-} + liftU2 = liftA2 + {-# INLINE liftU2 #-} + liftI2 = liftA2 + {-# INLINE liftI2 #-} instance Bind V3 where V3 a b c >>- f = V3 a' b' c' where @@ -83,8 +166,10 @@ {-# INLINE (>>-) #-} instance Monad V3 where +#if !(MIN_VERSION_base(4,11,0)) return a = V3 a a a {-# INLINE return #-} +#endif V3 a b c >>= f = V3 a' b' c' where V3 a' _ _ = f a V3 _ b' _ = f b @@ -115,6 +200,52 @@ fromRational = pure . fromRational {-# INLINE fromRational #-} +instance Floating a => Floating (V3 a) where + pi = pure pi + {-# INLINE pi #-} + exp = fmap exp + {-# INLINE exp #-} + sqrt = fmap sqrt + {-# INLINE sqrt #-} + log = fmap log + {-# INLINE log #-} + (**) = liftA2 (**) + {-# INLINE (**) #-} + logBase = liftA2 logBase + {-# INLINE logBase #-} + sin = fmap sin + {-# INLINE sin #-} + tan = fmap tan + {-# INLINE tan #-} + cos = fmap cos + {-# INLINE cos #-} + asin = fmap asin + {-# INLINE asin #-} + atan = fmap atan + {-# INLINE atan #-} + acos = fmap acos + {-# INLINE acos #-} + sinh = fmap sinh + {-# INLINE sinh #-} + tanh = fmap tanh + {-# INLINE tanh #-} + cosh = fmap cosh + {-# INLINE cosh #-} + asinh = fmap asinh + {-# INLINE asinh #-} + atanh = fmap atanh + {-# INLINE atanh #-} + acosh = fmap acosh + {-# INLINE acosh #-} + +instance Hashable a => Hashable (V3 a) where + hashWithSalt s (V3 a b c) = s `hashWithSalt` a `hashWithSalt` b `hashWithSalt` c + {-# INLINE hashWithSalt #-} + +instance Hashable1 V3 where + liftHashWithSalt h s (V3 a b c) = s `h` a `h` b `h` c + {-# INLINE liftHashWithSalt #-} + instance Metric V3 where dot (V3 a b c) (V3 d e f) = a * d + b * e + c * f {-# INLINABLE dot #-} @@ -126,19 +257,51 @@ -- | A space that distinguishes 3 orthogonal basis vectors: '_x', '_y', and '_z'. (It may have more) class R2 t => R3 t where -- | - -- @ - -- '_z' :: Lens' (t a) a - -- @ - _z :: Functor f => (a -> f a) -> t a -> f (t a) - -- | - -- @ - -- '_xyz' :: Lens' (t a) ('V3' a) - -- @ - _xyz :: Functor f => (V3 a -> f (V3 a)) -> t a -> f (t a) + -- >>> V3 1 2 3 ^. _z + -- 3 + _z :: Lens' (t a) a -instance R2 V3 where + _xyz :: Lens' (t a) (V3 a) + +_xz, _yz, _zx, _zy :: R3 t => Lens' (t a) (V2 a) + +_xz f = _xyz $ \(V3 a b c) -> f (V2 a c) <&> \(V2 a' c') -> V3 a' b c' +{-# INLINE _xz #-} + +_yz f = _xyz $ \(V3 a b c) -> f (V2 b c) <&> \(V2 b' c') -> V3 a b' c' +{-# INLINE _yz #-} + +_zx f = _xyz $ \(V3 a b c) -> f (V2 c a) <&> \(V2 c' a') -> V3 a' b c' +{-# INLINE _zx #-} + +_zy f = _xyz $ \(V3 a b c) -> f (V2 c b) <&> \(V2 c' b') -> V3 a b' c' +{-# INLINE _zy #-} + +_xzy, _yxz, _yzx, _zxy, _zyx :: R3 t => Lens' (t a) (V3 a) + +_xzy f = _xyz $ \(V3 a b c) -> f (V3 a c b) <&> \(V3 a' c' b') -> V3 a' b' c' +{-# INLINE _xzy #-} + +_yxz f = _xyz $ \(V3 a b c) -> f (V3 b a c) <&> \(V3 b' a' c') -> V3 a' b' c' +{-# INLINE _yxz #-} + +_yzx f = _xyz $ \(V3 a b c) -> f (V3 b c a) <&> \(V3 b' c' a') -> V3 a' b' c' +{-# INLINE _yzx #-} + +_zxy f = _xyz $ \(V3 a b c) -> f (V3 c a b) <&> \(V3 c' a' b') -> V3 a' b' c' +{-# INLINE _zxy #-} + +_zyx f = _xyz $ \(V3 a b c) -> f (V3 c b a) <&> \(V3 c' b' a') -> V3 a' b' c' +{-# INLINE _zyx #-} + +ez :: R3 t => E t +ez = E _z + +instance R1 V3 where _x f (V3 a b c) = (\a' -> V3 a' b c) <$> f a {-# INLINE _x #-} + +instance R2 V3 where _y f (V3 a b c) = (\b' -> V3 a b' c) <$> f b {-# INLINE _y #-} _xy f (V3 a b c) = (\(V2 a' b') -> V3 a' b' c) <$> f (V2 a b) @@ -150,10 +313,6 @@ _xyz = id {-# INLINE _xyz #-} -instance Core V3 where - core f = V3 (f _x) (f _y) (f _z) - {-# INLINE core #-} - instance Storable a => Storable (V3 a) where sizeOf _ = 3 * sizeOf (undefined::a) {-# INLINE sizeOf #-} @@ -202,3 +361,153 @@ inRange (l1,u1) i1 && inRange (l2,u2) i2 && inRange (l3,u3) i3 {-# INLINE inRange #-} + +instance Representable V3 where + type Rep V3 = E V3 + tabulate f = V3 (f ex) (f ey) (f ez) + {-# INLINE tabulate #-} + index xs (E l) = view l xs + {-# INLINE index #-} + +instance WithIndex.FunctorWithIndex (E V3) V3 where + imap f (V3 a b c) = V3 (f ex a) (f ey b) (f ez c) + {-# INLINE imap #-} + +instance WithIndex.FoldableWithIndex (E V3) V3 where + ifoldMap f (V3 a b c) = f ex a `mappend` f ey b `mappend` f ez c + {-# INLINE ifoldMap #-} + +instance WithIndex.TraversableWithIndex (E V3) V3 where + itraverse f (V3 a b c) = V3 <$> f ex a <*> f ey b <*> f ez c + {-# INLINE itraverse #-} + +#if !MIN_VERSION_lens(5,0,0) +instance Lens.FunctorWithIndex (E V3) V3 where imap = WithIndex.imap +instance Lens.FoldableWithIndex (E V3) V3 where ifoldMap = WithIndex.ifoldMap +instance Lens.TraversableWithIndex (E V3) V3 where itraverse = WithIndex.itraverse +#endif + +type instance Index (V3 a) = E V3 +type instance IxValue (V3 a) = a + +instance Ixed (V3 a) where + ix i = el i + {-# INLINE ix #-} + +instance Each (V3 a) (V3 b) a b where + each = traverse + {-# INLINE each #-} + +data instance U.Vector (V3 a) = V_V3 {-# UNPACK #-} !Int !(U.Vector a) +data instance U.MVector s (V3 a) = MV_V3 {-# UNPACK #-} !Int !(U.MVector s a) +instance U.Unbox a => U.Unbox (V3 a) + +instance U.Unbox a => M.MVector U.MVector (V3 a) where + {-# INLINE basicLength #-} + {-# INLINE basicUnsafeSlice #-} + {-# INLINE basicOverlaps #-} + {-# INLINE basicUnsafeNew #-} + {-# INLINE basicUnsafeRead #-} + {-# INLINE basicUnsafeWrite #-} + basicLength (MV_V3 n _) = n + basicUnsafeSlice m n (MV_V3 _ v) = MV_V3 n (M.basicUnsafeSlice (3*m) (3*n) v) + basicOverlaps (MV_V3 _ v) (MV_V3 _ u) = M.basicOverlaps v u + basicUnsafeNew n = liftM (MV_V3 n) (M.basicUnsafeNew (3*n)) + basicUnsafeRead (MV_V3 _ v) i = + do let o = 3*i + x <- M.basicUnsafeRead v o + y <- M.basicUnsafeRead v (o+1) + z <- M.basicUnsafeRead v (o+2) + return (V3 x y z) + basicUnsafeWrite (MV_V3 _ v) i (V3 x y z) = + do let o = 3*i + M.basicUnsafeWrite v o x + M.basicUnsafeWrite v (o+1) y + M.basicUnsafeWrite v (o+2) z + basicInitialize (MV_V3 _ v) = M.basicInitialize v + {-# INLINE basicInitialize #-} + +instance U.Unbox a => G.Vector U.Vector (V3 a) where + {-# INLINE basicUnsafeFreeze #-} + {-# INLINE basicUnsafeThaw #-} + {-# INLINE basicLength #-} + {-# INLINE basicUnsafeSlice #-} + {-# INLINE basicUnsafeIndexM #-} + basicUnsafeFreeze (MV_V3 n v) = liftM ( V_V3 n) (G.basicUnsafeFreeze v) + basicUnsafeThaw ( V_V3 n v) = liftM (MV_V3 n) (G.basicUnsafeThaw v) + basicLength ( V_V3 n _) = n + basicUnsafeSlice m n (V_V3 _ v) = V_V3 n (G.basicUnsafeSlice (3*m) (3*n) v) + basicUnsafeIndexM (V_V3 _ v) i = + do let o = 3*i + x <- G.basicUnsafeIndexM v o + y <- G.basicUnsafeIndexM v (o+1) + z <- G.basicUnsafeIndexM v (o+2) + return (V3 x y z) + +instance MonadZip V3 where + mzipWith = liftA2 + +instance MonadFix V3 where + mfix f = V3 (let V3 a _ _ = f a in a) + (let V3 _ a _ = f a in a) + (let V3 _ _ a = f a in a) + +instance Bounded a => Bounded (V3 a) where + minBound = pure minBound + {-# INLINE minBound #-} + maxBound = pure maxBound + {-# INLINE maxBound #-} + +instance NFData a => NFData (V3 a) where + rnf (V3 a b c) = rnf a `seq` rnf b `seq` rnf c + +instance Serial1 V3 where + serializeWith = traverse_ + deserializeWith k = V3 <$> k <*> k <*> k + +instance Serial a => Serial (V3 a) where + serialize = serializeWith serialize + deserialize = deserializeWith deserialize + +instance Binary a => Binary (V3 a) where + put = serializeWith Binary.put + get = deserializeWith Binary.get + +instance Serialize a => Serialize (V3 a) where + put = serializeWith Cereal.put + get = deserializeWith Cereal.get + +instance Eq1 V3 where + liftEq k (V3 a b c) (V3 d e f) = k a d && k b e && k c f +instance Ord1 V3 where + liftCompare k (V3 a b c) (V3 d e f) = k a d `mappend` k b e `mappend` k c f +instance Read1 V3 where + liftReadsPrec k _ d = readParen (d > 10) $ \r -> + [ (V3 a b c, r4) + | ("V3",r1) <- lex r + , (a,r2) <- k 11 r1 + , (b,r3) <- k 11 r2 + , (c,r4) <- k 11 r3 + ] +instance Show1 V3 where + liftShowsPrec f _ d (V3 a b c) = showParen (d > 10) $ + showString "V3 " . f 11 a . showChar ' ' . f 11 b . showChar ' ' . f 11 c + +instance Field1 (V3 a) (V3 a) a a where + _1 f (V3 x y z) = f x <&> \x' -> V3 x' y z + +instance Field2 (V3 a) (V3 a) a a where + _2 f (V3 x y z) = f y <&> \y' -> V3 x y' z + +instance Field3 (V3 a) (V3 a) a a where + _3 f (V3 x y z) = f z <&> \z' -> V3 x y z' + +instance Semigroup a => Semigroup (V3 a) where + (<>) = liftA2 (<>) + +instance Monoid a => Monoid (V3 a) where + mempty = pure mempty +#if !(MIN_VERSION_base(4,11,0)) + mappend = liftA2 mappend +#endif + diff --git a/src/Linear/V4.hs b/src/Linear/V4.hs --- a/src/Linear/V4.hs +++ b/src/Linear/V4.hs @@ -1,8 +1,18 @@ -{-# LANGUAGE DeriveDataTypeable, ScopedTypeVariables #-} +{-# LANGUAGE DeriveDataTypeable #-} +{-# LANGUAGE ScopedTypeVariables #-} +{-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE RankNTypes #-} +{-# LANGUAGE TypeFamilies #-} +{-# LANGUAGE MultiParamTypeClasses #-} +{-# LANGUAGE CPP #-} +{-# LANGUAGE Trustworthy #-} +{-# LANGUAGE DeriveGeneric #-} +{-# LANGUAGE DataKinds #-} +{-# LANGUAGE DeriveLift #-} + ----------------------------------------------------------------------------- -- | --- Module : Linear.V4 --- Copyright : (C) 2012-2013 Edward Kmett, +-- Copyright : (C) 2012-2015 Edward Kmett -- License : BSD-style (see the file LICENSE) -- -- Maintainer : Edward Kmett @@ -13,36 +23,85 @@ ---------------------------------------------------------------------------- module Linear.V4 ( V4(..) - , vector, point + , vector, point, normalizePoint + , R1(..) , R2(..) + , _yx , R3(..) + , _xz, _yz, _zx, _zy + , _xzy, _yxz, _yzx, _zxy, _zyx , R4(..) + , _xw, _yw, _zw, _wx, _wy, _wz + , _xyw, _xzw, _xwy, _xwz, _yxw, _yzw, _ywx, _ywz, _zxw, _zyw, _zwx, _zwy + , _wxy, _wxz, _wyx, _wyz, _wzx, _wzy + , _xywz, _xzyw, _xzwy, _xwyz, _xwzy, _yxzw , _yxwz, _yzxw, _yzwx, _ywxz + , _ywzx, _zxyw, _zxwy, _zyxw, _zywx, _zwxy, _zwyx, _wxyz, _wxzy, _wyxz + , _wyzx, _wzxy, _wzyx + , ex, ey, ez, ew ) where +#if !MIN_VERSION_base(4,18,0) import Control.Applicative +#endif +import Control.DeepSeq (NFData(rnf)) +import Control.Monad (liftM) +import Control.Monad.Fix +import Control.Monad.Zip +import Control.Lens as Lens hiding ((<.>)) +import Data.Binary as Binary +import Data.Bytes.Serial import Data.Data import Data.Distributive import Data.Foldable +import qualified Data.Foldable.WithIndex as WithIndex import Data.Functor.Bind +import Data.Functor.Classes +import Data.Functor.Rep +import qualified Data.Functor.WithIndex as WithIndex +import Data.Hashable +import Data.Hashable.Lifted +#if !(MIN_VERSION_base(4,11,0)) import Data.Semigroup +#endif import Data.Semigroup.Foldable -import Data.Semigroup.Traversable -import Data.Traversable +import Data.Serialize as Cereal +import qualified Data.Traversable.WithIndex as WithIndex +import qualified Data.Vector as V +import qualified Data.Vector.Generic.Mutable as M +import qualified Data.Vector.Generic as G +import qualified Data.Vector.Unboxed.Base as U import Foreign.Ptr (castPtr) import Foreign.Storable (Storable(..)) import GHC.Arr (Ix(..)) -import Linear.Core +import GHC.Generics (Generic, Generic1) +#if defined(MIN_VERSION_template_haskell) +import Language.Haskell.TH.Syntax (Lift) +#endif import Linear.Epsilon import Linear.Metric +import Linear.V import Linear.V2 import Linear.V3 import Linear.Vector +import System.Random (Random(..), Uniform) +import System.Random.Stateful (UniformRange(..)) -{-# ANN module "HLint: ignore Reduce duplication" #-} +-- $setup +-- >>> import Control.Lens hiding (index) -- | A 4-dimensional vector. -data V4 a = V4 a a a a deriving (Eq,Ord,Show,Read,Data,Typeable) +data V4 a = V4 !a !a !a !a deriving (Eq,Ord,Show,Read,Data + ,Generic,Generic1 +#if defined(MIN_VERSION_template_haskell) + ,Lift +#endif + ) +instance Finite V4 where + type Size V4 = 4 + toV (V4 a b c d) = V (V.fromListN 4 [a,b,c,d]) + fromV (V v) = V4 (v V.! 0) (v V.! 1) (v V.! 2) (v V.! 3) + instance Functor V4 where fmap f (V4 a b c d) = V4 (f a) (f b) (f c) (f d) {-# INLINE fmap #-} @@ -52,7 +111,34 @@ instance Foldable V4 where foldMap f (V4 a b c d) = f a `mappend` f b `mappend` f c `mappend` f d {-# INLINE foldMap #-} +#if MIN_VERSION_base(4,13,0) + foldMap' f (V4 a b c d) = ((f a `mappend` f b) `mappend` f c) `mappend` f d + {-# INLINE foldMap' #-} +#endif + null _ = False + length _ = 4 +instance Random a => Random (V4 a) where + random g = case random g of + (a, g') -> case random g' of + (b, g'') -> case random g'' of + (c, g''') -> case random g''' of + (d, g'''') -> (V4 a b c d, g'''') + randomR (V4 a b c d, V4 a' b' c' d') g = case randomR (a,a') g of + (a'', g') -> case randomR (b,b') g' of + (b'', g'') -> case randomR (c,c') g'' of + (c'', g''') -> case randomR (d,d') g''' of + (d'', g'''') -> (V4 a'' b'' c'' d'', g'''') + +instance Uniform a => Uniform (V4 a) where + +instance UniformRange a => UniformRange (V4 a) where + uniformRM (V4 a b c d, V4 a' b' c' d') g = V4 + <$> uniformRM (a, a') g + <*> uniformRM (b, b') g + <*> uniformRM (c, c') g + <*> uniformRM (d, d') g + instance Traversable V4 where traverse f (V4 a b c d) = V4 <$> f a <*> f b <*> f c <*> f d {-# INLINE traverse #-} @@ -75,7 +161,13 @@ V4 a b c d <.> V4 e f g h = V4 (a e) (b f) (c g) (d h) {-# INLINE (<.>) #-} -instance Additive V4 +instance Additive V4 where + zero = pure 0 + {-# INLINE zero #-} + liftU2 = liftA2 + {-# INLINE liftU2 #-} + liftI2 = liftA2 + {-# INLINE liftI2 #-} instance Bind V4 where V4 a b c d >>- f = V4 a' b' c' d' where @@ -86,8 +178,10 @@ {-# INLINE (>>-) #-} instance Monad V4 where +#if !(MIN_VERSION_base(4,11,0)) return a = V4 a a a a {-# INLINE return #-} +#endif V4 a b c d >>= f = V4 a' b' c' d' where V4 a' _ _ _ = f a V4 _ b' _ _ = f b @@ -119,6 +213,44 @@ fromRational = pure . fromRational {-# INLINE fromRational #-} +instance Floating a => Floating (V4 a) where + pi = pure pi + {-# INLINE pi #-} + exp = fmap exp + {-# INLINE exp #-} + sqrt = fmap sqrt + {-# INLINE sqrt #-} + log = fmap log + {-# INLINE log #-} + (**) = liftA2 (**) + {-# INLINE (**) #-} + logBase = liftA2 logBase + {-# INLINE logBase #-} + sin = fmap sin + {-# INLINE sin #-} + tan = fmap tan + {-# INLINE tan #-} + cos = fmap cos + {-# INLINE cos #-} + asin = fmap asin + {-# INLINE asin #-} + atan = fmap atan + {-# INLINE atan #-} + acos = fmap acos + {-# INLINE acos #-} + sinh = fmap sinh + {-# INLINE sinh #-} + tanh = fmap tanh + {-# INLINE tanh #-} + cosh = fmap cosh + {-# INLINE cosh #-} + asinh = fmap asinh + {-# INLINE asinh #-} + atanh = fmap atanh + {-# INLINE atanh #-} + acosh = fmap acosh + {-# INLINE acosh #-} + instance Metric V4 where dot (V4 a b c d) (V4 e f g h) = a * e + b * f + c * g + d * h {-# INLINE dot #-} @@ -130,22 +262,176 @@ (fmap (\(V4 _ _ _ w) -> w) f) {-# INLINE distribute #-} +instance Hashable a => Hashable (V4 a) where + hashWithSalt s (V4 a b c d) = s `hashWithSalt` a `hashWithSalt` b `hashWithSalt` c `hashWithSalt` d + {-# INLINE hashWithSalt #-} + +instance Hashable1 V4 where + liftHashWithSalt h s (V4 a b c d) = s `h` a `h` b `h` c `h` d + {-# INLINE liftHashWithSalt #-} + -- | A space that distinguishes orthogonal basis vectors '_x', '_y', '_z', '_w'. (It may have more.) class R3 t => R4 t where -- | - -- @ - -- '_w' :: Lens' (t a) a - -- @ - _w :: Functor f => (a -> f a) -> t a -> f (t a) - -- | - -- @ - -- '_xyzw' :: Lens' (t a) ('V4' a) - -- @ - _xyzw :: Functor f => (V4 a -> f (V4 a)) -> t a -> f (t a) + -- >>> V4 1 2 3 4 ^._w + -- 4 + _w :: Lens' (t a) a + _xyzw :: Lens' (t a) (V4 a) -instance R2 V4 where +_xw, _yw, _zw, _wx, _wy, _wz :: R4 t => Lens' (t a) (V2 a) +_xw f = _xyzw $ \(V4 a b c d) -> f (V2 a d) <&> \(V2 a' d') -> V4 a' b c d' +{-# INLINE _xw #-} + +_yw f = _xyzw $ \(V4 a b c d) -> f (V2 b d) <&> \(V2 b' d') -> V4 a b' c d' +{-# INLINE _yw #-} + +_zw f = _xyzw $ \(V4 a b c d) -> f (V2 c d) <&> \(V2 c' d') -> V4 a b c' d' +{-# INLINE _zw #-} + +_wx f = _xyzw $ \(V4 a b c d) -> f (V2 d a) <&> \(V2 d' a') -> V4 a' b c d' +{-# INLINE _wx #-} + +_wy f = _xyzw $ \(V4 a b c d) -> f (V2 d b) <&> \(V2 d' b') -> V4 a b' c d' +{-# INLINE _wy #-} + +_wz f = _xyzw $ \(V4 a b c d) -> f (V2 d c) <&> \(V2 d' c') -> V4 a b c' d' +{-# INLINE _wz #-} + +_xyw, _xzw, _xwy, _xwz, _yxw, _yzw, _ywx, _ywz, _zxw, _zyw, _zwx, _zwy, _wxy, _wxz, _wyx, _wyz, _wzx, _wzy :: R4 t => Lens' (t a) (V3 a) +_xyw f = _xyzw $ \(V4 a b c d) -> f (V3 a b d) <&> \(V3 a' b' d') -> V4 a' b' c d' +{-# INLINE _xyw #-} + +_xzw f = _xyzw $ \(V4 a b c d) -> f (V3 a c d) <&> \(V3 a' c' d') -> V4 a' b c' d' +{-# INLINE _xzw #-} + +_xwy f = _xyzw $ \(V4 a b c d) -> f (V3 a d b) <&> \(V3 a' d' b') -> V4 a' b' c d' +{-# INLINE _xwy #-} + +_xwz f = _xyzw $ \(V4 a b c d) -> f (V3 a d c) <&> \(V3 a' d' c') -> V4 a' b c' d' +{-# INLINE _xwz #-} + +_yxw f = _xyzw $ \(V4 a b c d) -> f (V3 b a d) <&> \(V3 b' a' d') -> V4 a' b' c d' +{-# INLINE _yxw #-} + +_yzw f = _xyzw $ \(V4 a b c d) -> f (V3 b c d) <&> \(V3 b' c' d') -> V4 a b' c' d' +{-# INLINE _yzw #-} + +_ywx f = _xyzw $ \(V4 a b c d) -> f (V3 b d a) <&> \(V3 b' d' a') -> V4 a' b' c d' +{-# INLINE _ywx #-} + +_ywz f = _xyzw $ \(V4 a b c d) -> f (V3 b d c) <&> \(V3 b' d' c') -> V4 a b' c' d' +{-# INLINE _ywz #-} + +_zxw f = _xyzw $ \(V4 a b c d) -> f (V3 c a d) <&> \(V3 c' a' d') -> V4 a' b c' d' +{-# INLINE _zxw #-} + +_zyw f = _xyzw $ \(V4 a b c d) -> f (V3 c b d) <&> \(V3 c' b' d') -> V4 a b' c' d' +{-# INLINE _zyw #-} + +_zwx f = _xyzw $ \(V4 a b c d) -> f (V3 c d a) <&> \(V3 c' d' a') -> V4 a' b c' d' +{-# INLINE _zwx #-} + +_zwy f = _xyzw $ \(V4 a b c d) -> f (V3 c d b) <&> \(V3 c' d' b') -> V4 a b' c' d' +{-# INLINE _zwy #-} + +_wxy f = _xyzw $ \(V4 a b c d) -> f (V3 d a b) <&> \(V3 d' a' b') -> V4 a' b' c d' +{-# INLINE _wxy #-} + +_wxz f = _xyzw $ \(V4 a b c d) -> f (V3 d a c) <&> \(V3 d' a' c') -> V4 a' b c' d' +{-# INLINE _wxz #-} + +_wyx f = _xyzw $ \(V4 a b c d) -> f (V3 d b a) <&> \(V3 d' b' a') -> V4 a' b' c d' +{-# INLINE _wyx #-} + +_wyz f = _xyzw $ \(V4 a b c d) -> f (V3 d b c) <&> \(V3 d' b' c') -> V4 a b' c' d' +{-# INLINE _wyz #-} + +_wzx f = _xyzw $ \(V4 a b c d) -> f (V3 d c a) <&> \(V3 d' c' a') -> V4 a' b c' d' +{-# INLINE _wzx #-} + +_wzy f = _xyzw $ \(V4 a b c d) -> f (V3 d c b) <&> \(V3 d' c' b') -> V4 a b' c' d' +{-# INLINE _wzy #-} + +_xywz, _xzyw, _xzwy, _xwyz, _xwzy, _yxzw , _yxwz, _yzxw, _yzwx, _ywxz + , _ywzx, _zxyw, _zxwy, _zyxw, _zywx, _zwxy, _zwyx, _wxyz, _wxzy, _wyxz + , _wyzx, _wzxy, _wzyx :: R4 t => Lens' (t a) (V4 a) +_xywz f = _xyzw $ \(V4 a b c d) -> f (V4 a b d c) <&> \(V4 a' b' d' c') -> V4 a' b' c' d' +{-# INLINE _xywz #-} + +_xzyw f = _xyzw $ \(V4 a b c d) -> f (V4 a c b d) <&> \(V4 a' c' b' d') -> V4 a' b' c' d' +{-# INLINE _xzyw #-} + +_xzwy f = _xyzw $ \(V4 a b c d) -> f (V4 a c d b) <&> \(V4 a' c' d' b') -> V4 a' b' c' d' +{-# INLINE _xzwy #-} + +_xwyz f = _xyzw $ \(V4 a b c d) -> f (V4 a d b c) <&> \(V4 a' d' b' c') -> V4 a' b' c' d' +{-# INLINE _xwyz #-} + +_xwzy f = _xyzw $ \(V4 a b c d) -> f (V4 a d c b) <&> \(V4 a' d' c' b') -> V4 a' b' c' d' +{-# INLINE _xwzy #-} + +_yxzw f = _xyzw $ \(V4 a b c d) -> f (V4 b a c d) <&> \(V4 b' a' c' d') -> V4 a' b' c' d' +{-# INLINE _yxzw #-} + +_yxwz f = _xyzw $ \(V4 a b c d) -> f (V4 b a d c) <&> \(V4 b' a' d' c') -> V4 a' b' c' d' +{-# INLINE _yxwz #-} + +_yzxw f = _xyzw $ \(V4 a b c d) -> f (V4 b c a d) <&> \(V4 b' c' a' d') -> V4 a' b' c' d' +{-# INLINE _yzxw #-} + +_yzwx f = _xyzw $ \(V4 a b c d) -> f (V4 b c d a) <&> \(V4 b' c' d' a') -> V4 a' b' c' d' +{-# INLINE _yzwx #-} + +_ywxz f = _xyzw $ \(V4 a b c d) -> f (V4 b d a c) <&> \(V4 b' d' a' c') -> V4 a' b' c' d' +{-# INLINE _ywxz #-} + +_ywzx f = _xyzw $ \(V4 a b c d) -> f (V4 b d c a) <&> \(V4 b' d' c' a') -> V4 a' b' c' d' +{-# INLINE _ywzx #-} + +_zxyw f = _xyzw $ \(V4 a b c d) -> f (V4 c a b d) <&> \(V4 c' a' b' d') -> V4 a' b' c' d' +{-# INLINE _zxyw #-} + +_zxwy f = _xyzw $ \(V4 a b c d) -> f (V4 c a d b) <&> \(V4 c' a' d' b') -> V4 a' b' c' d' +{-# INLINE _zxwy #-} + +_zyxw f = _xyzw $ \(V4 a b c d) -> f (V4 c b a d) <&> \(V4 c' b' a' d') -> V4 a' b' c' d' +{-# INLINE _zyxw #-} + +_zywx f = _xyzw $ \(V4 a b c d) -> f (V4 c b d a) <&> \(V4 c' b' d' a') -> V4 a' b' c' d' +{-# INLINE _zywx #-} + +_zwxy f = _xyzw $ \(V4 a b c d) -> f (V4 c d a b) <&> \(V4 c' d' a' b') -> V4 a' b' c' d' +{-# INLINE _zwxy #-} + +_zwyx f = _xyzw $ \(V4 a b c d) -> f (V4 c d b a) <&> \(V4 c' d' b' a') -> V4 a' b' c' d' +{-# INLINE _zwyx #-} + +_wxyz f = _xyzw $ \(V4 a b c d) -> f (V4 d a b c) <&> \(V4 d' a' b' c') -> V4 a' b' c' d' +{-# INLINE _wxyz #-} + +_wxzy f = _xyzw $ \(V4 a b c d) -> f (V4 d a c b) <&> \(V4 d' a' c' b') -> V4 a' b' c' d' +{-# INLINE _wxzy #-} + +_wyxz f = _xyzw $ \(V4 a b c d) -> f (V4 d b a c) <&> \(V4 d' b' a' c') -> V4 a' b' c' d' +{-# INLINE _wyxz #-} + +_wyzx f = _xyzw $ \(V4 a b c d) -> f (V4 d b c a) <&> \(V4 d' b' c' a') -> V4 a' b' c' d' +{-# INLINE _wyzx #-} + +_wzxy f = _xyzw $ \(V4 a b c d) -> f (V4 d c a b) <&> \(V4 d' c' a' b') -> V4 a' b' c' d' +{-# INLINE _wzxy #-} + +_wzyx f = _xyzw $ \(V4 a b c d) -> f (V4 d c b a) <&> \(V4 d' c' b' a') -> V4 a' b' c' d' +{-# INLINE _wzyx #-} + +ew :: R4 t => E t +ew = E _w + +instance R1 V4 where _x f (V4 a b c d) = (\a' -> V4 a' b c d) <$> f a {-# INLINE _x #-} + +instance R2 V4 where _y f (V4 a b c d) = (\b' -> V4 a b' c d) <$> f b {-# INLINE _y #-} _xy f (V4 a b c d) = (\(V2 a' b') -> V4 a' b' c d) <$> f (V2 a b) @@ -163,10 +449,6 @@ _xyzw = id {-# INLINE _xyzw #-} -instance Core V4 where - core f = V4 (f _x) (f _y) (f _z) (f _w) - {-# INLINE core #-} - instance Storable a => Storable (V4 a) where sizeOf _ = 4 * sizeOf (undefined::a) {-# INLINE sizeOf #-} @@ -183,16 +465,27 @@ where ptr' = castPtr ptr {-# INLINE peek #-} --- | Convert a 3-dimensional affine vector into a 4-dimensional homogeneous vector. +-- | Convert a 3-dimensional affine vector into a 4-dimensional homogeneous vector, +-- i.e. sets the @w@ coordinate to 0. vector :: Num a => V3 a -> V4 a vector (V3 a b c) = V4 a b c 0 {-# INLINE vector #-} --- | Convert a 3-dimensional affine point into a 4-dimensional homogeneous vector. +-- | Convert a 3-dimensional affine point into a 4-dimensional homogeneous vector, +-- i.e. sets the @w@ coordinate to 1. point :: Num a => V3 a -> V4 a point (V3 a b c) = V4 a b c 1 {-# INLINE point #-} +-- | Convert 4-dimensional projective coordinates to a 3-dimensional +-- point. This operation may be denoted, @euclidean [x:y:z:w] = (x\/w, +-- y\/w, z\/w)@ where the projective, homogenous, coordinate +-- @[x:y:z:w]@ is one of many associated with a single point @(x\/w, +-- y\/w, z\/w)@. +normalizePoint :: Fractional a => V4 a -> V3 a +normalizePoint (V4 a b c w) = (1/w) *^ V3 a b c +{-# INLINE normalizePoint #-} + instance Epsilon a => Epsilon (V4 a) where nearZero = nearZero . quadrance {-# INLINE nearZero #-} @@ -219,3 +512,147 @@ inRange (l1,u1) i1 && inRange (l2,u2) i2 && inRange (l3,u3) i3 && inRange (l4,u4) i4 {-# INLINE inRange #-} + +instance Representable V4 where + type Rep V4 = E V4 + tabulate f = V4 (f ex) (f ey) (f ez) (f ew) + {-# INLINE tabulate #-} + index xs (E l) = view l xs + {-# INLINE index #-} + +instance WithIndex.FunctorWithIndex (E V4) V4 where + imap f (V4 a b c d) = V4 (f ex a) (f ey b) (f ez c) (f ew d) + {-# INLINE imap #-} + +instance WithIndex.FoldableWithIndex (E V4) V4 where + ifoldMap f (V4 a b c d) = f ex a `mappend` f ey b `mappend` f ez c `mappend` f ew d + {-# INLINE ifoldMap #-} + +instance WithIndex.TraversableWithIndex (E V4) V4 where + itraverse f (V4 a b c d) = V4 <$> f ex a <*> f ey b <*> f ez c <*> f ew d + {-# INLINE itraverse #-} + +#if !MIN_VERSION_lens(5,0,0) +instance Lens.FunctorWithIndex (E V4) V4 where imap = WithIndex.imap +instance Lens.FoldableWithIndex (E V4) V4 where ifoldMap = WithIndex.ifoldMap +instance Lens.TraversableWithIndex (E V4) V4 where itraverse = WithIndex.itraverse +#endif + +type instance Index (V4 a) = E V4 +type instance IxValue (V4 a) = a + +instance Ixed (V4 a) where + ix i = el i + +instance Each (V4 a) (V4 b) a b where + each = traverse + +data instance U.Vector (V4 a) = V_V4 {-# UNPACK #-} !Int !(U.Vector a) +data instance U.MVector s (V4 a) = MV_V4 {-# UNPACK #-} !Int !(U.MVector s a) +instance U.Unbox a => U.Unbox (V4 a) + +instance U.Unbox a => M.MVector U.MVector (V4 a) where + basicLength (MV_V4 n _) = n + basicUnsafeSlice m n (MV_V4 _ v) = MV_V4 n (M.basicUnsafeSlice (4*m) (4*n) v) + basicOverlaps (MV_V4 _ v) (MV_V4 _ u) = M.basicOverlaps v u + basicUnsafeNew n = liftM (MV_V4 n) (M.basicUnsafeNew (4*n)) + basicUnsafeRead (MV_V4 _ v) i = + do let o = 4*i + x <- M.basicUnsafeRead v o + y <- M.basicUnsafeRead v (o+1) + z <- M.basicUnsafeRead v (o+2) + w <- M.basicUnsafeRead v (o+3) + return (V4 x y z w) + basicUnsafeWrite (MV_V4 _ v) i (V4 x y z w) = + do let o = 4*i + M.basicUnsafeWrite v o x + M.basicUnsafeWrite v (o+1) y + M.basicUnsafeWrite v (o+2) z + M.basicUnsafeWrite v (o+3) w + basicInitialize (MV_V4 _ v) = M.basicInitialize v + +instance U.Unbox a => G.Vector U.Vector (V4 a) where + basicUnsafeFreeze (MV_V4 n v) = liftM ( V_V4 n) (G.basicUnsafeFreeze v) + basicUnsafeThaw ( V_V4 n v) = liftM (MV_V4 n) (G.basicUnsafeThaw v) + basicLength ( V_V4 n _) = n + basicUnsafeSlice m n (V_V4 _ v) = V_V4 n (G.basicUnsafeSlice (4*m) (4*n) v) + basicUnsafeIndexM (V_V4 _ v) i = + do let o = 4*i + x <- G.basicUnsafeIndexM v o + y <- G.basicUnsafeIndexM v (o+1) + z <- G.basicUnsafeIndexM v (o+2) + w <- G.basicUnsafeIndexM v (o+3) + return (V4 x y z w) + +instance MonadZip V4 where + mzipWith = liftA2 + +instance MonadFix V4 where + mfix f = V4 (let V4 a _ _ _ = f a in a) + (let V4 _ a _ _ = f a in a) + (let V4 _ _ a _ = f a in a) + (let V4 _ _ _ a = f a in a) + +instance Bounded a => Bounded (V4 a) where + minBound = pure minBound + {-# INLINE minBound #-} + maxBound = pure maxBound + {-# INLINE maxBound #-} + +instance NFData a => NFData (V4 a) where + rnf (V4 a b c d) = rnf a `seq` rnf b `seq` rnf c `seq` rnf d + +instance Serial1 V4 where + serializeWith = traverse_ + deserializeWith k = V4 <$> k <*> k <*> k <*> k + +instance Serial a => Serial (V4 a) where + serialize = serializeWith serialize + deserialize = deserializeWith deserialize + +instance Binary a => Binary (V4 a) where + put = serializeWith Binary.put + get = deserializeWith Binary.get + +instance Serialize a => Serialize (V4 a) where + put = serializeWith Cereal.put + get = deserializeWith Cereal.get + +instance Eq1 V4 where + liftEq k (V4 a b c d) (V4 e f g h) = k a e && k b f && k c g && k d h +instance Ord1 V4 where + liftCompare k (V4 a b c d) (V4 e f g h) = k a e `mappend` k b f `mappend` k c g `mappend` k d h +instance Read1 V4 where + liftReadsPrec k _ z = readParen (z > 10) $ \r -> + [ (V4 a b c d, r5) + | ("V4",r1) <- lex r + , (a,r2) <- k 11 r1 + , (b,r3) <- k 11 r2 + , (c,r4) <- k 11 r3 + , (d,r5) <- k 11 r4 + ] +instance Show1 V4 where + liftShowsPrec f _ z (V4 a b c d) = showParen (z > 10) $ + showString "V4 " . f 11 a . showChar ' ' . f 11 b . showChar ' ' . f 11 c . showChar ' ' . f 11 d + +instance Field1 (V4 a) (V4 a) a a where + _1 f (V4 x y z w) = f x <&> \x' -> V4 x' y z w + +instance Field2 (V4 a) (V4 a) a a where + _2 f (V4 x y z w) = f y <&> \y' -> V4 x y' z w + +instance Field3 (V4 a) (V4 a) a a where + _3 f (V4 x y z w) = f z <&> \z' -> V4 x y z' w + +instance Field4 (V4 a) (V4 a) a a where + _4 f (V4 x y z w) = f w <&> \w' -> V4 x y z w' + +instance Semigroup a => Semigroup (V4 a) where + (<>) = liftA2 (<>) + +instance Monoid a => Monoid (V4 a) where + mempty = pure mempty +#if !(MIN_VERSION_base(4,11,0)) + mappend = liftA2 mappend +#endif + diff --git a/src/Linear/Vector.hs b/src/Linear/Vector.hs --- a/src/Linear/Vector.hs +++ b/src/Linear/Vector.hs @@ -1,9 +1,14 @@ {-# LANGUAGE CPP #-} +{-# LANGUAGE TypeOperators #-} +{-# LANGUAGE FlexibleContexts #-} +{-# LANGUAGE RankNTypes #-} +{-# LANGUAGE ScopedTypeVariables #-} +{-# LANGUAGE TypeFamilies #-} +{-# LANGUAGE Trustworthy #-} {-# LANGUAGE DefaultSignatures #-} ----------------------------------------------------------------------------- -- | --- Module : Linear.Vector --- Copyright : (C) 2012 Edward Kmett +-- Copyright : (C) 2012-2015 Edward Kmett -- License : BSD-style (see the file LICENSE) -- Maintainer : Edward Kmett -- Stability : provisional @@ -13,41 +18,103 @@ ----------------------------------------------------------------------------- module Linear.Vector ( Additive(..) + , E(..) , negated , (^*) , (*^) , (^/) + , sumV , basis , basisFor + , scaled + , outer + , unit ) where import Control.Applicative +import Control.Lens import Data.Complex -import Data.Foldable (foldMap) -import Data.Functor.Bind -import Data.Functor.Identity +import Data.Foldable as Foldable (forM_, foldl') +import Data.Functor.Compose +import Data.Functor.Product import Data.HashMap.Lazy as HashMap import Data.Hashable import Data.IntMap as IntMap import Data.Map as Map -import Data.Monoid (Sum(..)) -import Data.Traversable (Traversable, mapAccumL) +import qualified Data.Vector as Vector +import Data.Vector (Vector) +import qualified Data.Vector.Mutable as Mutable +import GHC.Generics import Linear.Instances () -- $setup --- >>> import Control.Lens -- >>> import Linear.V2 +-- | Basis element +newtype E t = E { el :: forall x. Lens' (t x) x } + infixl 6 ^+^, ^-^ infixl 7 ^*, *^, ^/ +class GAdditive f where + gzero :: Num a => f a + gliftU2 :: (a -> a -> a) -> f a -> f a -> f a + gliftI2 :: (a -> b -> c) -> f a -> f b -> f c + +instance GAdditive U1 where + gzero = U1 + {-# INLINE gzero #-} + gliftU2 _ U1 U1 = U1 + {-# INLINE gliftU2 #-} + gliftI2 _ U1 U1 = U1 + {-# INLINE gliftI2 #-} + +instance (GAdditive f, GAdditive g) => GAdditive (f :*: g) where + gzero = gzero :*: gzero + {-# INLINE gzero #-} + gliftU2 f (a :*: b) (c :*: d) = gliftU2 f a c :*: gliftU2 f b d + {-# INLINE gliftU2 #-} + gliftI2 f (a :*: b) (c :*: d) = gliftI2 f a c :*: gliftI2 f b d + {-# INLINE gliftI2 #-} + +instance (Additive f, GAdditive g) => GAdditive (f :.: g) where + gzero = Comp1 $ gzero <$ (zero :: f Int) + {-# INLINE gzero #-} + gliftU2 f (Comp1 a) (Comp1 b) = Comp1 $ liftU2 (gliftU2 f) a b + {-# INLINE gliftU2 #-} + gliftI2 f (Comp1 a) (Comp1 b) = Comp1 $ liftI2 (gliftI2 f) a b + {-# INLINE gliftI2 #-} + +instance Additive f => GAdditive (Rec1 f) where + gzero = Rec1 zero + {-# INLINE gzero #-} + gliftU2 f (Rec1 g) (Rec1 h) = Rec1 (liftU2 f g h) + {-# INLINE gliftU2 #-} + gliftI2 f (Rec1 g) (Rec1 h) = Rec1 (liftI2 f g h) + {-# INLINE gliftI2 #-} + +instance GAdditive f => GAdditive (M1 i c f) where + gzero = M1 gzero + {-# INLINE gzero #-} + gliftU2 f (M1 g) (M1 h) = M1 (gliftU2 f g h) + {-# INLINE gliftU2 #-} + gliftI2 f (M1 g) (M1 h) = M1 (gliftI2 f g h) + {-# INLINE gliftI2 #-} + +instance GAdditive Par1 where + gzero = Par1 0 + gliftU2 f (Par1 a) (Par1 b) = Par1 (f a b) + {-# INLINE gliftU2 #-} + gliftI2 f (Par1 a) (Par1 b) = Par1 (f a b) + {-# INLINE gliftI2 #-} + -- | A vector is an additive group with additional structure. -class Bind f => Additive f where +class Functor f => Additive f where -- | The zero vector zero :: Num a => f a #ifndef HLINT - default zero :: (Applicative f, Num a) => f a - zero = pure 0 + default zero :: (GAdditive (Rep1 f), Generic1 f, Num a) => f a + zero = to1 gzero #endif -- | Compute the sum of two vectors @@ -55,48 +122,162 @@ -- >>> V2 1 2 ^+^ V2 3 4 -- V2 4 6 (^+^) :: Num a => f a -> f a -> f a -#ifndef HLINT - default (^+^) :: (Applicative f, Num a) => f a -> f a -> f a - (^+^) = liftA2 (+) + (^+^) = liftU2 (+) {-# INLINE (^+^) #-} -#endif -- | Compute the difference between two vectors -- - -- >>> V2 4 5 - V2 3 1 + -- >>> V2 4 5 ^-^ V2 3 1 -- V2 1 4 (^-^) :: Num a => f a -> f a -> f a -#ifndef HLINT - default (^-^) :: (Applicative f, Num a) => f a -> f a -> f a - (^-^) = liftA2 (-) - {-# INLINE (^-^) #-} -#endif + x ^-^ y = x ^+^ negated y -- | Linearly interpolate between two vectors. + -- + -- /Since linear version 1.23, interpolation direction has been reversed; now/ + -- + -- > lerp 0 a b == a + -- > lerp 1 a b == b lerp :: Num a => a -> f a -> f a -> f a - lerp alpha u v = alpha *^ u ^+^ (1 - alpha) *^ v + lerp alpha u v = (1 - alpha) *^ u ^+^ alpha *^ v {-# INLINE lerp #-} + -- | Apply a function to merge the 'non-zero' components of two vectors, unioning the rest of the values. + -- + -- * For a dense vector this is equivalent to 'liftA2'. + -- + -- * For a sparse vector this is equivalent to 'unionWith'. + liftU2 :: (a -> a -> a) -> f a -> f a -> f a +#ifndef HLINT + default liftU2 :: Applicative f => (a -> a -> a) -> f a -> f a -> f a + liftU2 = liftA2 + {-# INLINE liftU2 #-} +#endif + + -- | Apply a function to the components of two vectors. + -- + -- * For a dense vector this is equivalent to 'liftA2'. + -- + -- * For a sparse vector this is equivalent to 'intersectionWith'. + liftI2 :: (a -> b -> c) -> f a -> f b -> f c +#ifndef HLINT + default liftI2 :: Applicative f => (a -> b -> c) -> f a -> f b -> f c + liftI2 = liftA2 + {-# INLINE liftI2 #-} +#endif + +instance (Additive f, Additive g) => Additive (Product f g) where + zero = Pair zero zero + liftU2 f (Pair a b) (Pair c d) = Pair (liftU2 f a c) (liftU2 f b d) + liftI2 f (Pair a b) (Pair c d) = Pair (liftI2 f a c) (liftI2 f b d) + Pair a b ^+^ Pair c d = Pair (a ^+^ c) (b ^+^ d) + Pair a b ^-^ Pair c d = Pair (a ^-^ c) (b ^-^ d) + lerp alpha (Pair a b) (Pair c d) = Pair (lerp alpha a c) (lerp alpha b d) + +instance (Additive f, Additive g) => Additive (Compose f g) where + zero = Compose $ zero <$ (zero :: f Int) + {-# INLINE zero #-} + Compose a ^+^ Compose b = Compose $ liftU2 (^+^) a b + {-# INLINE (^+^) #-} + Compose a ^-^ Compose b = Compose $ liftU2 (^-^) a b + {-# INLINE (^-^) #-} + liftU2 f (Compose a) (Compose b) = Compose $ liftU2 (liftU2 f) a b + {-# INLINE liftU2 #-} + liftI2 f (Compose a) (Compose b) = Compose $ liftI2 (liftI2 f) a b + {-# INLINE liftI2 #-} + +instance Additive ZipList where + zero = ZipList [] + {-# INLINE zero #-} + liftU2 f (ZipList xs) (ZipList ys) = ZipList (liftU2 f xs ys) + {-# INLINE liftU2 #-} + liftI2 = liftA2 + {-# INLINE liftI2 #-} + +instance Additive Vector where + zero = mempty + {-# INLINE zero #-} + liftU2 f u v = case compare lu lv of + LT | lu == 0 -> v + | otherwise -> Vector.modify (\ w -> Foldable.forM_ [0..lu-1] $ \i -> Mutable.unsafeWrite w i $ f (Vector.unsafeIndex u i) (Vector.unsafeIndex v i)) v + EQ -> Vector.zipWith f u v + GT | lv == 0 -> u + | otherwise -> Vector.modify (\ w -> Foldable.forM_ [0..lv-1] $ \i -> Mutable.unsafeWrite w i $ f (Vector.unsafeIndex u i) (Vector.unsafeIndex v i)) u + where + lu = Vector.length u + lv = Vector.length v + {-# INLINE liftU2 #-} + liftI2 = Vector.zipWith + {-# INLINE liftI2 #-} + +instance Additive Maybe where + zero = Nothing + {-# INLINE zero #-} + liftU2 f (Just a) (Just b) = Just (f a b) + liftU2 _ Nothing ys = ys + liftU2 _ xs Nothing = xs + {-# INLINE liftU2 #-} + liftI2 = liftA2 + {-# INLINE liftI2 #-} + +instance Additive [] where + zero = [] + {-# INLINE zero #-} + liftU2 f = go where + go (x:xs) (y:ys) = f x y : go xs ys + go [] ys = ys + go xs [] = xs + {-# INLINE liftU2 #-} + liftI2 = Prelude.zipWith + {-# INLINE liftI2 #-} + instance Additive IntMap where zero = IntMap.empty - (^+^) = IntMap.unionWith (+) - xs ^-^ ys = IntMap.unionWith (+) xs (negated ys) + {-# INLINE zero #-} + liftU2 = IntMap.unionWith + {-# INLINE liftU2 #-} + liftI2 = IntMap.intersectionWith + {-# INLINE liftI2 #-} instance Ord k => Additive (Map k) where zero = Map.empty - (^+^) = Map.unionWith (+) - xs ^-^ ys = Map.unionWith (+) xs (negated ys) + {-# INLINE zero #-} + liftU2 = Map.unionWith + {-# INLINE liftU2 #-} + liftI2 = Map.intersectionWith + {-# INLINE liftI2 #-} instance (Eq k, Hashable k) => Additive (HashMap k) where zero = HashMap.empty - (^+^) = HashMap.unionWith (+) - xs ^-^ ys = HashMap.unionWith (+) xs (negated ys) + {-# INLINE zero #-} + liftU2 = HashMap.unionWith + {-# INLINE liftU2 #-} + liftI2 = HashMap.intersectionWith + {-# INLINE liftI2 #-} -instance Additive ((->) b) +instance Additive ((->) b) where + zero = const 0 + {-# INLINE zero #-} + liftU2 = liftA2 + {-# INLINE liftU2 #-} + liftI2 = liftA2 + {-# INLINE liftI2 #-} -instance Additive Complex +instance Additive Complex where + zero = 0 :+ 0 + {-# INLINE zero #-} + liftU2 f (a :+ b) (c :+ d) = f a c :+ f b d + {-# INLINE liftU2 #-} + liftI2 f (a :+ b) (c :+ d) = f a c :+ f b d + {-# INLINE liftI2 #-} -instance Additive Identity +instance Additive Identity where + zero = Identity 0 + {-# INLINE zero #-} + liftU2 = liftA2 + {-# INLINE liftU2 #-} + liftI2 = liftA2 + {-# INLINE liftI2 #-} -- | Compute the negation of a vector -- @@ -106,6 +287,14 @@ negated = fmap negate {-# INLINE negated #-} +-- | Sum over multiple vectors +-- +-- >>> sumV [V2 1 1, V2 3 4] +-- V2 4 5 +sumV :: (Foldable f, Additive v, Num a) => f (v a) -> v a +sumV = Foldable.foldl' (^+^) zero +{-# INLINE sumV #-} + -- | Compute the left scalar product -- -- >>> 2 *^ V2 3 4 @@ -127,23 +316,39 @@ f ^/ a = fmap (/a) f {-# INLINE (^/) #-} --- @setElement i x v@ sets the @i@'th element of @v@ to @x@. -setElement :: Traversable t => Int -> a -> t a -> t a -setElement i x = snd . mapAccumL aux 0 - where aux j y = let j' = j + 1 - y' = if i == j then x else y - in j' `seq` (j', y') - -- | Produce a default basis for a vector space. If the dimensionality -- of the vector space is not statically known, see 'basisFor'. -basis :: (Applicative t, Traversable t, Num a) => [t a] -basis = [ setElement k 1 z | k <- [0..n - 1] ] - where z = pure 0 - n = getSum $ foldMap (const (Sum 1)) z +basis :: (Additive t, Traversable t, Num a) => [t a] +basis = basisFor (zero :: Additive v => v Int) -- | Produce a default basis for a vector space from which the -- argument is drawn. -basisFor :: (Traversable t, Enum a, Num a) => t a -> [t a] -basisFor v = [ setElement k 1 z | k <- [0..n-1] ] - where z = 0 <$ v - n = getSum $ foldMap (const (Sum 1)) v +basisFor :: (Traversable t, Num a) => t b -> [t a] +basisFor = \t -> + ifoldMapOf traversed ?? t $ \i _ -> + return $ + iover traversed ?? t $ \j _ -> + if i == j then 1 else 0 +{-# INLINABLE basisFor #-} + +-- | Produce a diagonal (scale) matrix from a vector. +-- +-- >>> scaled (V2 2 3) +-- V2 (V2 2 0) (V2 0 3) +scaled :: (Traversable t, Num a) => t a -> t (t a) +scaled = \t -> iter t (\i x -> iter t (\j _ -> if i == j then x else 0)) + where + iter :: Traversable t => t a -> (Int -> a -> b) -> t b + iter x f = iover traversed f x +{-# INLINE scaled #-} + +-- | Create a unit vector. +-- +-- >>> unit _x :: V2 Int +-- V2 1 0 +unit :: (Additive t, Num a) => ASetter' (t a) a -> t a +unit l = set' l 1 zero + +-- | Outer (tensor) product of two vectors +outer :: (Functor f, Functor g, Num a) => f a -> g a -> f (g a) +outer a b = fmap (\x->fmap (*x) b) a diff --git a/tests/Prop/Quaternion.hs b/tests/Prop/Quaternion.hs new file mode 100644 --- /dev/null +++ b/tests/Prop/Quaternion.hs @@ -0,0 +1,28 @@ +{-# OPTIONS_GHC -Wno-orphans #-} +module Prop.Quaternion (tests) where + +import Linear.Quaternion (Quaternion(..)) +import Linear.Epsilon (nearZero) +import Linear.Vector (lerp) +import Test.QuickCheck (Arbitrary(..)) +import Test.Tasty (TestTree, testGroup) +import Test.Tasty.QuickCheck (testProperty) + +import Prop.V3 () + +instance Arbitrary a => Arbitrary (Quaternion a) where + arbitrary = Quaternion <$> arbitrary <*> arbitrary + +prop_lerp0 :: Quaternion Double -> Quaternion Double -> Bool +prop_lerp0 a b = nearZero (lerp 0 a b - a) + +prop_lerp1 :: Quaternion Double -> Quaternion Double -> Bool +prop_lerp1 a b = nearZero (lerp 1 a b - b) + +tests :: [TestTree] +tests = + [ testGroup "lerp" + [ testProperty "lerp 0 a b == a" prop_lerp0 + , testProperty "lerp 1 a b == b" prop_lerp1 + ] + ] diff --git a/tests/Prop/V3.hs b/tests/Prop/V3.hs new file mode 100644 --- /dev/null +++ b/tests/Prop/V3.hs @@ -0,0 +1,8 @@ +{-# OPTIONS_GHC -Wno-orphans #-} +module Prop.V3 () where + +import Linear.V3 (V3(..)) +import Test.QuickCheck (Arbitrary(..)) + +instance Arbitrary a => Arbitrary (V3 a) where + arbitrary = V3 <$> arbitrary <*> arbitrary <*> arbitrary diff --git a/tests/Test.hs b/tests/Test.hs new file mode 100644 --- /dev/null +++ b/tests/Test.hs @@ -0,0 +1,24 @@ +{-# LANGUAGE CPP #-} +module Main (main) where + +import Test.Tasty (defaultMain, testGroup, TestTree) + +import qualified Prop.Quaternion +import qualified Unit.Binary +import qualified Unit.Plucker +import qualified Unit.V + +tests :: [TestTree] +tests = + [ testGroup "Property tests" + [ testGroup "Quaternion" Prop.Quaternion.tests + ] + , testGroup "Unit tests" + [ testGroup "Binary" Unit.Binary.tests + , testGroup "Plucker" Unit.Plucker.tests + , testGroup "V" Unit.V.tests + ] + ] + +main :: IO () +main = defaultMain $ testGroup "linear" tests diff --git a/tests/Unit/Binary.hs b/tests/Unit/Binary.hs new file mode 100644 --- /dev/null +++ b/tests/Unit/Binary.hs @@ -0,0 +1,20 @@ +module Unit.Binary (tests) where + +import Data.Binary.Put +import Data.Binary.Get +import Linear +import qualified Data.ByteString.Lazy as BS +import Test.Tasty (TestTree) +import Test.Tasty.HUnit ((@?=), testCase) + +originalVecs :: (V3 Float, V2 Char) +originalVecs = (V3 1 2 3, V2 'a' 'b') + +bytes :: BS.ByteString +bytes = runPut $ do putLinear $ fst originalVecs + putLinear $ snd originalVecs + +tests :: [TestTree] +tests = [ testCase "Serialized length" $ BS.length bytes @?= 3*13+2 + , testCase "Deserialization" $ deserialized @?= originalVecs ] + where deserialized = runGet ((,) <$> getLinear <*> getLinear) bytes diff --git a/tests/Unit/Plucker.hs b/tests/Unit/Plucker.hs new file mode 100644 --- /dev/null +++ b/tests/Unit/Plucker.hs @@ -0,0 +1,36 @@ +module Unit.Plucker (tests) where +import Linear +import Linear.Plucker +import Linear.Plucker.Coincides +import Test.Tasty (TestTree) +import Test.Tasty.HUnit ((@?=), testCase) + +ln2,ln3,ln4,ln5,ln6,ln7,ln8,ln9 :: Plucker Float +ln2 = plucker3D (V3 1 3 0) (V3 1 3 (-2)) -- starting line +ln3 = plucker3D (V3 2 3 0) (V3 2 3 (-2)) -- parallel +ln4 = plucker3D (V3 2 4 0) (V3 1 4 (-2)) -- ccw +ln5 = plucker3D (V3 (-2) 4 0) (V3 2 4 (-2)) -- cw +ln6 = plucker3D (V3 2 3 0) (V3 1 3 (-2)) -- intersect +ln7 = plucker3D (V3 1 3 0) (V3 1 3 2) -- reversed +ln8 = plucker3D (V3 0 4 4) (V3 0 (-4) (-4)) -- through origin +ln9 = Plucker 1 2 3 4 5 6 -- not a 3D line + +tests :: [TestTree] +tests = [ testCase "parallel" $ parallel ln2 ln3 @?= True + , testCase "CCW" $ passes ln2 ln4 @?= Counterclockwise + , testCase "CW" $ passes ln2 ln5 @?= Clockwise + , testCase "intersect1" $ intersects ln2 ln6 @?= True + , testCase "intersect2" $ intersects ln2 ln3 @?= False + , testCase "line equality 1" $ Line ln2 == Line ln2 @?= True + , testCase "line equality 2" $ Line ln2 == Line ln7 @?= True + , testCase "line equality 3" $ Line ln2 == Ray ln7 @?= True + , testCase "line equality 4" $ Ray ln2 == Line ln7 @?= True + , testCase "ray equality 1" $ Ray ln2 == Ray ln7 @?= False + , testCase "ray equality 2" $ Ray ln2 == Ray (3 *^ ln2) @?= True + , testCase "ray equality 3" $ Ray ln2 == Ray (negate ln7) @?= True + , testCase "quadrance" $ nearZero (quadranceToOrigin ln2 - 10) @?= True + , testCase "closest 1" $ + nearZero (qd (V3 1 3 0) $ closestToOrigin ln2) @?= True + , testCase "closest 2" $ nearZero (qd 0 $ closestToOrigin ln8) @?= True + , testCase "isLine 1" $ isLine ln2 @?= True + , testCase "isLine 2" $ isLine ln9 @?= False ] diff --git a/tests/Unit/V.hs b/tests/Unit/V.hs new file mode 100644 --- /dev/null +++ b/tests/Unit/V.hs @@ -0,0 +1,14 @@ +{-# LANGUAGE DataKinds #-} +module Unit.V (tests) where + +import Control.DeepSeq (rnf) +import qualified Data.Vector.Unboxed as U (fromList) +import Linear.V (V) +import Test.Tasty (TestTree) +import Test.Tasty.HUnit ((@?=), testCase) + +v10 :: V 10 Int +v10 = return 5 + +tests :: [TestTree] +tests = [ testCase "GH124" $ rnf (U.fromList [v10]) @?= () ] diff --git a/tests/doctests.hs b/tests/doctests.hs --- a/tests/doctests.hs +++ b/tests/doctests.hs @@ -1,30 +1,19 @@ +----------------------------------------------------------------------------- +-- | +-- Module : Main (doctests) +-- Copyright : (C) 2012-14 Edward Kmett +-- License : BSD-style (see the file LICENSE) +-- Maintainer : Edward Kmett +-- Stability : provisional +-- Portability : portable +-- +-- This module exists to add dependencies +----------------------------------------------------------------------------- module Main where -import Build_doctests (deps) -import Control.Applicative -import Control.Monad -import Data.List -import System.Directory -import System.FilePath -import Test.DocTest - main :: IO () -main = getSources >>= \sources -> doctest $ - "-isrc" - : "-idist/build/autogen" - : "-optP-include" - : "-optPdist/build/autogen/cabal_macros.h" - : "-hide-all-packages" - : map ("-package="++) deps ++ sources - -getSources :: IO [FilePath] -getSources = filter (isSuffixOf ".hs") <$> go "src" - where - go dir = do - (dirs, files) <- getFilesAndDirectories dir - (files ++) . concat <$> mapM go dirs - -getFilesAndDirectories :: FilePath -> IO ([FilePath], [FilePath]) -getFilesAndDirectories dir = do - c <- map (dir ) . filter (`notElem` ["..", "."]) <$> getDirectoryContents dir - (,) <$> filterM doesDirectoryExist c <*> filterM doesFileExist c +main = do + putStrLn "This test-suite exists only to add dependencies" + putStrLn "To run doctests: " + putStrLn " cabal build all --enable-tests" + putStrLn " cabal-docspec" diff --git a/travis/cabal-apt-install b/travis/cabal-apt-install deleted file mode 100644 --- a/travis/cabal-apt-install +++ /dev/null @@ -1,16 +0,0 @@ -#!/bin/sh -set -eu - -sudo apt-get -q update -sudo apt-get -q -y install dctrl-tools - -# Try installing some of the build-deps with apt-get for speed. -eval "$( - printf '%s' "grep-aptavail -n -sPackage '(' -FFALSE -X FALSE ')'" - 2>/dev/null cabal install "$@" --dry-run -v | \ - sed -nre "s/^([^ ]+)-[0-9.]+ \(.*$/ -o '(' -FPackage -X libghc-\1-dev ')'/p" | \ - xargs -d'\n' -)" | sort -u | xargs -d'\n' sudo apt-get -q -y install -- libghc-quickcheck2-dev - -# Install whatever is still needed with cabal. -cabal install "$@" diff --git a/travis/config b/travis/config deleted file mode 100644 --- a/travis/config +++ /dev/null @@ -1,16 +0,0 @@ --- This provides a custom ~/.cabal/config file for use when hackage is down that should work on unix --- --- This is particularly useful for travis-ci to get it to stop complaining --- about a broken build when everything is still correct on our end. --- --- This uses Luite Stegeman's mirror of hackage provided by his 'hdiff' site instead --- --- To enable this, uncomment the before_script in .travis.yml - -remote-repo: hdiff.luite.com:http://hdiff.luite.com/packages/archive -remote-repo-cache: ~/.cabal/packages -world-file: ~/.cabal/world -build-summary: ~/.cabal/logs/build.log -remote-build-reporting: anonymous -install-dirs user -install-dirs global